What he said. The G# trill key has no effect on the spring tension or responsiveness of the G# key; the trill key itself is unsprung and it's basically just along for the ride. Sometimes if the corks in the G# trill mechanism are lost, the G# trill key can kind of stick up and be felt in between your other fingers. In this case, the real fix is just to install a correct thickness cork where the mechanism wants it, and taking off the key altogether would be like using a cannon to swat a fly. Besides that, depending on how the individual design is, you might actually have to cut the key off which would be a mutilation. I would suggest checking the corks and then if desired gently bending it down closer to the body to get it more out of the way.
Since both the index and middle fingers of the right hand only ever touch one key touch, if your hand position is correct, you should never encounter that trill key in the normal course of playing. My Conn alto and tenor both have this key and I have never noticed it while playing.