Is this true? I just wonder what is underneath it. I wouldn't mind peeling the entire lot off and being done with it.

 

Yes it's true those were most likely added on by the dealer when new. I just bought a 97 Tahoe for our daughter to drive and it has the same warped and peeling wood. I suppose you could peel off the one panel that is warped and see if the glue/tape will come off without finish damage. If the finish is not good underneath the wood you could reapply the piece.

 

I would put it on something flat like a workbench and slowly start heating it with a heat gun. Don't get it so hot that it melts but just warm enough to flatten it out. Then use good 3M auto double sided trim adhesive to put them back on-the stuff with the red backing and looks black/grey.