At what altitude, if any, may an ultralight overfly the Gallup airport (KGUP) with no prior authorization without violating FAR 103.17?
You can not fly an ultralight there without prior authorization if I am reading 103.17 correctly. The way that I am reading this, it seems that you may not be in controlled airspace around an airport without prior authorization, period. And, above  18000 is a no-go as well. 

The highest concentration of aircraft traffic is at airports, Navaids like VORs, and on airways. You want to steer clear of those unless you are in clear and direct communication with those in charge of the airspace. Gallup has all three.

As far as Class E airspace, the way that 103.17 reads, It makes it sound like you are not allowed to fly in any Class E airspace over an airport without prior authorization. Admittedly, it’s splitting hairs. Everywhere else in 14 CFR, the description of Surface Class E has slightly different verbiage. 


  103.17 Operations in certain airspace.
  No person may operate an ultralight vehicle within Class A, Class B, Class C, or Class D airspace or within the lateral boundaries of the surface area of Class E airspace designated for an airport unless that person has prior authorization from the ATC facility having jurisdiction over that airspace.  
  
  137.43 Operations in controlled airspace designated for an airport.
  (b) No person may operate an aircraft in weather conditions below VFR minimums within the lateral boundaries of a Class E airspace area that extends upward from the surface unless authorization for that operation has been obtained from the ATC facility having jurisdiction over that area.  
  
  3–2–6 Class E Airspace
  1. Surface area designated for an airport where a control tower is not in operation. Class E surface areas extend upward from the surface to a designated altitude, or to the adjacent or overlying controlled airspace. The airspace will be configured to contain all instrument procedures.