Plunger might work. Or tap tap tappity from the inside with rubber mallet, boards, rolling tennis balls, lacrosse balls over it, etc. It'll be super wavy and obvious, but if you're just looking for a backyard fix that makes it slightly less caved in, you might get somewhere. Paint might chip or flake off bending it back. Otherwise, send pics to a PDR person that isn't part of a big company and they might cut you a deal for "this is the best I can to for that damage." Or a small body shop.
I doubt you're going to make it look much less obvious by yourself. What's your purpose for popping them out?