It's no glitch.
Simply a stray vertice. When you 'selected' the polys that you wanted to texture, of course the poly connected to that vertice was also selected.
The fix? Fix it!
You simply have a poly (and it's vertices) that is out of place. You just need to back out of your texturing, un-select all your polys, go back into editable mesh (or whichever mode your using), find and fix that poly.
Any modifers that you add to the parts 'stack' can be removed. A simple caution though...gmax doesn't like steps taken that confuses it! If you do some kind of step...in the wrong way...gmax can lock-up, and you can lose the model.
Just use a little common sense, and carefully 'un-do' your steps. Like the polys you have selected (to texture), un-select them...then remove the modifyer.
All no big deal. Takes a lot longer to talk about it...than doing it. Simple things that all of us run across, so don't worry about it. Just takes getting used to gmax, and all it's workings.
So far...your work looks good!