I went to look at my rear wiper motor just now. I had no trouble getting the trim panel off, but there's a black plate that's over the guts of the tailgate, and I can't tell how it was put on, never mind how to get it off without taking a sawzall to it. The fasteners seem like they're meant to be fastened from the other, inaccessible side.

I'm sure this is a stupid question, but I stood there scratching my head for a while before giving up. How do I get this undone?

 

Push in on the center portion of each retainer, then remove. Reset the retainer by pushing the center portion back out the top so that it is now protruding from the top of the fastener.

 

Are you sure? They're not pushing...no matter how hard I lean on them.

 

on a 95 blazer the metal pice is held on by bolts

 

Some drill out the center and chisel the heads off the rivets. I usually use a whiz wheel and grind the heads off them.
Refastening style is up to you.
Harbor freight has inexpensive 1/4 inch rivets and tool. Or...you could twist and turn and use regular bolt and nut fasteners.