Can't remove wires from a circuit breaker
The dilemma: do I cut the load neutral at the breaker, or is there a way to remove it from the breaker?  

Remember: the load line is purple; the load neutral is white; the panel neutral is white with a black stripe; the short loop from one side of the breaker to the other is dark grey (may look black in the photos).


The first 3 photos (below) show different angles of all 4 wires and where they connect to this ITE GFCI breaker. Notice: There are 3 ports where the wires connect. 3 wires (the white, the striped and one end of the grey loop) enter a single port. The purple and the other end of the grey loop have their own port for connection.  


https://i.stack.imgur.com/M2OWE.jpg  
https://i.stack.imgur.com/0LGLP.jpg  
https://i.stack.imgur.com/5oVE0.jpg  


The second photo (above) also shows the top of two set-screws. (Look at the breaker in the middle of the three shown.) The one on the right releases the line load (purple) wire, and looks normal. The one on the left releases the stand-alone end of the grey wire loop; but you can't see any groove for a screwdriver or other tool because ITE put a cover/block over the head of the screw. Clearly, they don't want someone removing that screw, especially accidentally.
The third photo (above): Look at the broad side of the breaker. Notice 4 small shallow holes with something somewhat bright inside each one. These bright objects are either rivets or another type of fastener that either hold the breaker case together or hold internal parts to the breaker case.

I mention this because when I found no set-screw(s) to release the 3 wires in the same port, I looked for a hole in which to insert a tool to push on some kind of spring release of the wires. As you can see, there is no such hole, and this is the broad side of the breaker closest to those 3 wires. You can also see fairly well, from all of the first 3 photos, that there is no such hole on the thin side of the breaker to which all the wires attach. There are also no such holes on the opposite broad side of the breaker (no photo).
The fourth photo (below) shows the same broad side of the breaker as above. Notice:


You can see all 4 wires just above the top of the image of the breaker.
You can see two of the four rivets/fasteners.
You can see 3 embossed labels. I couldn't get a half-decent photo of these labels, but...


The one just under the 3 wires in the same port identifies those wires. It says, one under another: "Load Lug", "Plain Wire - Load Neut.", "Stripe Wire - Neut. Bus"
The one in the center of the breaker includes "Use only UL approved..." and "ITE Imperial Corp...Pennsylvania".
The one in the upper left corner says "STRIP GAGE" and has an embossed line of the length to strip the wires.

There are a few identifying codes stamped in white, not all still entirely legible, even in person.  



https://i.stack.imgur.com/OWLui.jpg


In the fifth photo (below):


You can see directly into the 2 set-screw ports, and see that you can see the screwdriver slot at the top of the set-screw on the right, but not the one on the left, which is covered/blocked. (There's no need to access the one on the left in order to replace the breaker.)
The L-shaped yellowish-brownish area below the set-screws is the residue from the glued-on breaker label, which came off during my handling of the breaker, probably when I pulled off the tape that I used to hold the switch in the off position while working. The label included:

i) "Class A 1 Pole Unit Issue A-345"

ii) "Current Interrupting Rating"

iii) "Gould Corp. Circuit Protection Division Philadelphia, Penn. USA"

iv) "I-T-E Circuit Breaker &amp; Ground Fault Circuit Interrupter"

v) "CAT. NO. OFI-B015" (The letter "O" may actually the number zero and the letter "I" may actually be the number "1" in "OFI". The number
"0" may actually be the letter "O" in "B015". I think I got it right, but my own handwriting is unclear and I don't have the label anymore to double-check it.)  



https://i.stack.imgur.com/KRyjj.jpg


In the sixth photo (below), our breaker is the highest one. Notice:


You can see all 4 wires.
If you follow the white load neutral, you can see that it connects with either two other wires or a split wire, which is/are grey, under a yellow wire nut.  
(Note: These wires at the wire nut are irrelevant to changing the breaker, except in one case:  If the load neutral has to be cut from the breaker and it ends up too short to reach the new breaker when that breaker is properly attached to the panel, then you have to replace the load neutral (white) wire with a longer wire (of the same/correct gauge), which means undoing the wire nut to remove the "far" end of the old load neutral wire and replace it with the "far" end of the new load neutral wire.)
It's not all in the picture, but if you carefully follow the striped panel neutral, you can see that it heads downward, then curves back upward and proceeds above the breaker, along the right edge of the line of the breakers. (It's hard to see the highest part.)  



https://i.stack.imgur.com/Ah9J6.jpg  

7)  In the seventh photo (below), the breaker is not installed into the panel. Notice:  


You can see the striped panel neutral where it went above the breaker and finally turns and connects to the neutral bar.  
You can see the yellow wire nut containing the "far" end of the load neutral (white) and the two grey wires. (It's hard to see both grey wires.)  
In the lower left corner of the image, you can see the empty slot from which the breaker was removed.  


https://i.stack.imgur.com/YOQP4.jpg  

8) The eighth photo (below) shows the utility side of the breaker.  Notice:  


You can see the white "TEST" button and the ON/OFF switch of this GFCI breaker.
You can see the yellowish L-shaped area where the glued-on label used to be.  
You can see part of the "back" broad side and two of the four 'rivet-holes' there.  There are no holes to insert a tool to press a spring to release those 3 wires in the single port.  


https://i.stack.imgur.com/EYi8v.jpg  

I included all the details I could about this breaker for those who really want to "see" what I've been looking at and who may want to research further.  Especially, because the issue was finding a way to remove the load neutral from the breaker, I wanted to show you every square inch of the breaker so you could look for yourself.  

It turns out that one of my relatives has a friend who has been a master electrician for over 40 years, has lived in this area for his whole life, has not only worked for many years for the county where this house is located, but done so as an electrician and as an electrical inspector.  He agreed to come here to give me some honest input about some significant electrical work we have been considering doing. ("Honest", because he is a good friend of my relative and because he will not be doing the work.)  

I also informed him that I need help with the breaker.  I sent him a photo at his request because he also couldn't picture it from my description.  

Before he arrived, I saw a former neighbor and good acquaintance who also happens to be a master electrician who I trust, also with over 40 years' experience.  I described the breaker to him, and he was also puzzled by my description.  

When the electrician arrived, we went right to the breaker.  He turned it every which way to look it over, then looked where each wire led.  After assessing everything, he told me he had never seen a breaker like this, not the short wire loop and not the 3 wires in a single port.  Then, he confirmed what seemed obvious to me as the answer to my question, but what I did not want to act on without such confirmation:  

There is no way to release those 3 wires.  The load line has to be cut at the breaker. (Fortunately, after cutting it, it was still long enough to reach the new breaker.)  

The design of this breaker may be a dinosaur that went extinct long ago.