Gell-based paint stripper. Doesn't leave any 'oily' residue like Goo-Off / other stuff so the new overlay will still stick.
You will need to rough up the plastic to let the chemicals get in underneath (use a wallpaper "tiger" device to poke thousands of holes through the plastic), or you can use a wide putty knife to get under it as well and let the stripper get under the leading edge bit by bit.