I think Grey's talking about the gas cap door.  You should just be able to unscrew the painted bit from the hinge.

Skeered me there for a minute. Although I've never liked the stock "ugly" gas cap I thought for a minute I had an additional stock option that I had not considered.
One of these days though it's gonna go and somefin shiny will be sittin in it's place.

The answer to your inquiry depends on how original you want to keep your 'vette. If you can obtain a new OEM bumper (75's front and rear are still available at least through Ecklers, only '74 fronts OEM are available, rears are no longer made with urethane that I have been able to find), that is your best bet as it has the same feel and texture as the original. It also comes with some short-comings such as 1) it is hard to match paint on urethane to paint on fiberglas. Even the new vettes that had urethane bumpers quickly develop tint differences in the bumper versus the fiberglas and 2) they too shall rot, although that is a 25-30 year process typically. Nothing you can do about that as far as I have been able to determine.

As someone in this thead notes, patience is the key to removal. I would re-emphasize the use of a lubricant such as PB or Liquid Wrench on each of the 18+ bolts that hold the nuts on securing the rear bumper. The first thing you might want to do, as I did, is get a Dremel or similar tool with a couple of brush heads and clean the threads of each of the bolts. Otherwise, you will twist several, if not all, of the bolts off during removal. This won't be a big deal if you don't intend to re-use the mounting brackets, but if you are trying to go back as close to original as possible, you will probably want to try to salvage the original retaining brackets. Once you have cleaned the threads, turn the nut off as far as it will until it gets too tight to move easily, then back it to its original position and clean some more. Remember, you are bringing 30 years of corrosion and dirt forward with each turn. I got all of the nuts off except for one without twisting a bolt off. It took some time, but once the new bumper is on, it takes a lot of inspection (as long as you don't touch it-fiberglass versus urethane) to tell that it is not original.

LIkewise, patience is the key to fitting the new bumper.The flex-fit fiberglass versus the rigid is well worth the extra money as you can move areas of the bumper to get a closer fit minimizing the amount of grinding, filling and sanding you would have to do with a rigid bumper. Then, by working each bolt area back on individually, you should get an acceptable fit. The marking of each hole as you clamp and bolt each previous hole seemed to be the key for my application. The saving grace is if you don't get a good fit on an individual hole, fiberglas is not hard to repair so you just fill the mis-fit hole and re-drill it.

Hope this helps some and good luck.