So is it the whole car you want to remove the paint from or just the bumpers?
If it was paint code 180 on the above chart, what a shame to change it.
You will not save the original paint below the cheapy paint job. The only methods for removing it are, sanding, media blast like RA40 says to do, chemical paint remover, total body dipping in caustic chemicals.
If your real careful and want to spend months (with very fine sand paper) you can carefully sand it to the old paint and if the paint place left you any clear coat you could restore it. Also I have played with the idea of reapplying a new clear coat. In the older days I remember out fits offering a clear coat to protect the factory paint and in those days it was a single stage baked on enamel of some sort. Nowdays I think all new cars have a pimer that is a urethane and then a water base, base coat (strictly air dry crap it is, and adhesion to the primer is very questionable) then a urethane clear top coat. I don't know what the LS used for the base or color coat. We need Yamae to go visit the factory some day and ask them.