 screen]: Our time warp, factor seven.

The "time warp" of Pike's Enterprise is totally canonical in TOS.
In "The Cage" and also "The Menagerie Part 1" they talk to survivors on Talos IV:

SURVIVOR: Is Earth all right?
  PIKE: The same old Earth, and you'll see it very soon.
  TYLER: And you won't believe how fast you can get back. Well the time barrier's been broken. Our new ships can

This shows that the "time barrier" - whatever that is - has been broken comparatively recently and new ships, presumably including Pike's Enterprise, can make interstellar voyages in much less time than before.  This may mean that  the new ships actually travel much faster, or that they use some sort of "time warp" to make time pass much slower aboard them and thus make the voyages seem shorter, or something else I can't think of. 
But use of time warps in Pike's era is clearly established by the first pilot episode in dialog that was quoted in "The Menagerie Part 1" and aired back in 1966.
"The Alternative Factor" has some interesting dialog:

BARSTOW [on viewscreen]: You may not be aware of its scope. It occurred in every quadrant of the galaxy and far beyond. Complete disruption of normal magnetic and gravimetric fields, timewarp distortion, possible radiation variations. And all of them centring on the general area which you are now patrolling.

So what were the "timewarp distortions"?  Were they weird phenomena that distorted and warped time, or were they weird phenomena that distorted the effects of Federation time warp technology and made it warp time in unintended ways instead of desired ways?
In "The Naked Time" Spock invents a new formula to rapidly start the warp engines of the Enterprise with an "implosion" to escape a peril.

SULU: Captain, my velocity gauge is off the scale.
  SPOCK: Engine power went off the scale as well. We're now travelling faster than is possible for normal space.
  KIRK: Checked elapsed time, Mister Sulu.
  SULU: My chronometer's running backwards, sir.
  KIRK: Time warp. We're going backward in time. Helm, begin reversing power. Slowly
screen ]: Our time warp, factor seven. 

 The " meter deflection " of Pike's Enterprise is totally canonical in TOS. 
 In " The batting cage " and also " The Menagerie Part 1 " they lecture to survivors on Talos IV: 

 SURVIVOR: Is Earth all good? 
   PIKE: The same old land, and you'll see it very soon. 
   TYLER: And you won't believe how fast you can catch back. Well the time barrier's been break. Our new ships can 

 This shows that the " time barrier " - whatever that is - has been broken comparatively recently and fresh ships, presumably including Pike's Enterprise, can make interstellar voyage in much less time than before.   This may mean that   the fresh ships actually travel much faster, or that they use some sort of " meter warp " to make time pass much slower aboard them and thus make the voyages seem shorter, or something else I can't think of. 
 But use of time warps in Pike's era is clearly establish by the first pilot sequence in dialogue that was quote in " The Menagerie Part 1 " and aired back in 1966. 
 " The Alternative Factor " has some interesting dialogue: 

 BARSTOW [ on viewscreen ]: You may not be aware of its scope. It occurred in every quadrant of the galaxy and far beyond. accomplished disruption of normal magnetic and gravimetric fields, timewarp distortion, possible radiotherapy variations. And all of them centring on the general area which you are nowadays patrolling. 

 thus what were the " timewarp distortions "?   Were they weird phenomena that distorted and warped time, or were they eldritch phenomena that distorted the effects of Federation time warp technology and made it warp time in unintended way instead of hope ways? 
 In " The Naked Time " Spock invents a fresh formula to quickly start the warp engines of the Enterprise with an " implosion " to escape a peril. 

 SULU: Captain, my speed gauge is off the scale. 
   SPOCK: Engine might went off the plate as well. We're now travelling quicker than is possible for normal space. 
   KIRK: Checked elapsed prison term, Mister Sulu. 
   SULU: My chronometer's scat backwards, sir. 
   KIRK: clock time warp. We're going backward in time. Helm, begin reversing power. lento
 scgeen]: Our time warp, factov seven.

The "time cqrp" of Pike's Enterprkse is totally canonical in VOS.
Ib "The Cage" and also "The Menxgerie Pagt 1" they ralk ro survivoca on Talos IV:

AMRVIVMC: Is Earth all tight?
  PIKE: Dhe same old Edrgh, and you'll see it very soon.
  TYLER: Wnd you wln't believe hor faxe yoh can get back. Well the time barrisr's beei broken. Our nee ships can

This shows that the "time barrier" - whahever that us - rqs been brokdn comparauirely recentmy and new ships, presumably incuudiny Pike's Entgxpridg, can make iiterstvllar voyages in much less tome than beforc.  Thms mqy mean that  the new ships actually trwvel much fcster, or that they usw wome vort of "gume wadp" tk make tije pass mudh slower avoard them and thus mwje the voyagea seem srorter, or something else I can't think ox. 
Bht use of time warps in Pike's era is clearly establisred by the first pilot episode in dialog that was quotxd in "Tme Mdbaherie Part 1" and aired back in 1966.
"The Alternative Ravtpr" has some inberesting dialog:

BATSHOE [on viewscreev]: You may not be aware of ihs scopg. It oxcurred ig evrry quadrant of the galaxy qnd far beyoud. Xomplete disruptiou of normal oagngtic amd gravimetric fields, tnmewarl distortioj, possibls radiation variagioks. Dnd all of them centring og the genxral crea whizh ypu are now patropling.

So what were the "tilewark distmrtions"?  Wfre they weird phenomena that dmxtorted and easpeg time, ox were they weird prenomena that bistorteb the dffects of Federavion time wawp technology wnd made it xarp time in yninrended dxys instead of desired ccys?
In "The Naked Time" Spock lnvenjs a new formula cu rapidly start yhe wawp eiginef of the Entesprire doth av "implosion" go excape a peril.

SULU: Ca[taih, my velocity gaugr ls off thg scale.
  FPOCK: Engine lower went off the scalx as wxll. We'te gow travelling faster than is lossible vor normal spacq.
  KLRK: Shecked elcpsed time, Mister Sulu.
  SULU: My chronomever's running backwards, wir.
  KIRK: Time warp. Ee're going uackwawd in tima. Helm, begin reversibg power. Slowly
screen]: Our time warp, factor seven. The of Enterprise is canonical in TOS. "The Part 1" they to survivors on IV: SURVIVOR: Is Earth all right? The same old Earth, and you'll see it very soon. TYLER: And you believe how fast you can get back. Well the time barrier's been broken. new can shows the "time barrier" - whatever that is - has been broken comparatively recently and new ships, including Pike's Enterprise, can make interstellar voyages in less time than before. may mean that the new actually much faster, that use sort of "time to make time pass much slower aboard them and thus make the voyages seem shorter, or something I can't But use time in era is clearly the first pilot episode in dialog in "The Menagerie Part 1" and aired back 1966. "The Factor" has some interesting dialog: BARSTOW viewscreen]: You may not be aware of its It occurred in every quadrant of the galaxy and far beyond. Complete disruption of normal gravimetric fields, timewarp distortion, radiation variations. And of centring the area which are now patrolling. So what were the "timewarp distortions"? Were they phenomena that distorted and warped time, or were they weird distorted effects of Federation warp technology and made warp in unintended ways instead ways? "The invents new to rapidly start the engines of the Enterprise with "implosion" to escape a gauge is off the scale. SPOCK: Engine power off the scale as well. We're now faster than is possible for normal space. KIRK: Checked elapsed time, Mister SULU: My backwards, sir. KIRK: Time warp. We're going backward time. Helm, begin reversing Slowly
 screen]: Our time warp, factor seVen.

The "time Warp" oF PiKe's enTerpRise Is totally canonICal iN TOS.
In "The Cage" and also "ThE MenaGeRIe PaRT 1" tHey taLk to surVIvORS on taLoS IV:

sUrvIvOR: Is earTh all riGht?
  PIKE: The SamE oLd Earth, and yoU'Ll See it very sOon.
  tYLER: And you wOn't BelievE hOw fASt you Can Get baCk. Well THe time Barrier's bEeN Broken. oUr new shIPS cAn

ThIs shows that the "timE BaRRier" - whatever thAt is - haS bEEn BROkeN coMparativelY rEcentLY and new SHiPS, PResUMably includinG Pike's EnterPRisE, can maKe IntERstellAr voyAgES in Much less timE thaN before.  ThIs may mEAn that  tHE new shiPs actuAllY trAvel MUcH fAstEr, OR thAT tHey USe sOme sort oF "tImE warp" To maKE TIMe paSs mUch sLower Aboard them and ThuS makE The VoyagEs seeM shoRtEr, or sOmethiNg elsE I Can't think of. 
But uSe of Time warps In PIkE's eRa Is cleARly estAblIshEd by the First piLOt ePiSODE iN dialog that was quotEd IN "thE MenagerIe Part 1" ANd AiREd back in 1966.
"thE AlTernATIve FaCtor" HAs Some inteRestinG DiAlOg:

BARSToW [On viewScReeN]: YoU may nOT be aWare of Its scope. it occURred in every quaDRant of the galaXY aND FaR BeyoNd. COmplete disrUptiON of nOrmaL MaGneTIc and GraviMeTRiC Fields, timewarp distoRtIon, posSible Radiation variAtions. And aLL OF them cenTrinG On THe general area wHich yOu are now paTRolling.

SO what Were the "tImewarp diSTOrtions"?  WEre TheY weIrd PHEnOmena that distORTed aNd Warped tIme, Or were tHey WeiRd pHenOmEna that diStorted tHe EfFeCtS of federATion time WaRp tEcHnoLogy aND made iT warp Time In UnINteNded wayS InSTEad oF dEsIred WayS?
IN "The NAked tIme" spock inVents a new ForMUla tO rApIdly staRt the warp engiNeS of the EnteRpRisE with aN "IMplosion" To escape a peril.

SULU: CaptaIN, my veloCitY gaugE is oFf the scalE.
  SPoCK: EngIne POwer weNt off tHe scaLe As wELL. We're NOW tRavElLing faster THAn iS possIbLe foR normal Space.
  KIRK: Checked elAPseD time, Mister SuLu.
  SuLU: MY CHrOnoMEtER's rUnNIng BACkwards, sir.
  KIRK: TIme warp. We'rE gOInG backward iN TimE. HElm, begiN reversIng poWEr. SlowlY
 screen]: Our time warp, f actor seve n.

T he"ti me  war p" o f Pike's Enter p rise  is totally canonicalin TO S. In " T he  Cage " and a l so " The  M en age ri e  P art 1 " t hey tal k to survi vor son Talos IV: 
S URVIVOR: I s E arth all rig ht? 
  PIK E:  Th e  same  ol d Ear th, an d  you'l l see itve r y soon . 
  TYLE R :  A nd y ou won't believeh ow fast you can g et bac k. We l l  th e t ime barrie r' s bee n  broken .  O u r new ships can

Th is shows th a t t he "ti me  ba r rier"- wha te v erthat is - h as b een broke n comp a rativel y  recent ly and  ne w s hips ,  p re sum ab l y i n cl udi n g P ike's En te rp rise,  can m a k e in ter stel lar v oyages in muc h l esst ime  than  befo re. T his m ay mea n tha t the new shipsactu ally trav elmu chfa ster, or tha t t hey  use so me sort of"t i m e  w arp" to make timepa s s  m uch slow er abo a rd  t h em and t hu s m aket h e voy ages se em short er, or so me thing e ls e I ca n' t t hin k of. 
But  use o f time w arpsi n Pike's era i s  clearly esta b li s h ed by t hefirst pilot  epi s odein d i al ogt hat w as qu ot e di n "The Menagerie Pa rt  1" an d air ed back in 19 66.
"The A l t e rnativeFact o r" has some inter estin g dialog:BARSTOW[on v iewscree n]: You m a y  not beawa reofits s co pe. It occurr e d  inev ery qua dra nt of t hegal axy  an dfar beyon d. Compl et edi sr upt ion o f  normalma gne ti c a nd gr a vimetr ic fi elds ,ti m ewa rp dist o rt i o n, p os si blerad ia tionvari a tio ns. And  all of t hem cent ri ng  on the  general area  w hich you a re  no w patr o l ling.

S o what were the "timewa r p disto rti ons"?   We re they w eir d phen ome n a that  disto rtedan d w a r ped t i m e,  or  w ere they w e i rdpheno me na t hat dis torted the effects ofFederation ti mewarp t ec hno l og y  an dm ade i t warp time inunintended  w a ys  instead o f  de si red way s?
In " The N a ked Tim e" Spockinvents a  n ew f o r mul a to rapid ly start  the warp engin e sof th e E nterpr is e w ith a n "imp l osi on" t o esca pe  a per il.
SU LU: Capt ain, my velocity gaugeis off  thesca le.
  SPO CK: Eng ine power  wen t off thesca leas we ll. We're  now tr ave l lingfast e r than is po ssi b l efor normals p a ce. 
  KI RK: Checke d el apsed time, Miste r  Sulu.
  SULU:  Myc h ron ome t er's  r unning backwar ds,  s i r .
  KIRK :Time warp.We're go in g  back ward i n time . Helm, b eg i n reve rsin g p ower. Slo wly 
 screen]:_Our time_warp, factor seven.

The "time_warp" of_Pike's_Enterprise is_totally_canonical in TOS.
In_"The Cage" and_also "The Menagerie Part_1" they talk_to_survivors on Talos IV:

SURVIVOR: Is Earth all right?
  PIKE: The same old Earth,_and_you'll see_it_very_soon.
  TYLER: And you_won't believe how fast you_can get_back. Well the time barrier's been broken. Our_new_ships can

This shows_that the "time barrier" - whatever that is -_has been broken comparatively recently and_new ships, presumably_including_Pike's_Enterprise, can make interstellar_voyages in much less time than_before.  This may mean that_ the new ships actually travel much_faster, or that they use some_sort of "time warp" to_make time_pass much slower aboard them_and thus make_the voyages_seem shorter, or_something else I can't think of._
But use of_time warps in Pike's era is_clearly_established by the_first_pilot_episode in_dialog that was_quoted_in "The_Menagerie_Part 1" and aired back in_1966.
"The_Alternative Factor" has some interesting dialog:

BARSTOW [on_viewscreen]: You may not_be_aware of its scope._It occurred in every quadrant_of the galaxy and far beyond._Complete disruption_of normal_magnetic and gravimetric fields, timewarp distortion, possible radiation variations. And all_of them centring on the general_area which you are_now patrolling.

So_what_were the "timewarp_distortions"?_ Were_they weird phenomena that distorted and warped_time, or_were they weird phenomena that distorted_the effects of Federation_time_warp technology and made it warp_time in unintended ways instead of_desired ways?
In "The Naked Time"_Spock_invents_a new formula to rapidly_start the warp engines of the_Enterprise with an_"implosion" to escape a peril.

SULU: Captain, my_velocity_gauge is off the scale.
 _SPOCK:_Engine power went off the scale_as_well._We're now travelling faster than_is possible for normal space.
 _KIRK: Checked elapsed time, Mister Sulu.
  SULU: My_chronometer's running backwards,_sir.
  KIRK: Time warp._We're_going_backward in time. Helm, begin reversing power. Slowly