Trash it. Plain and simple.
You can try all you want to save the "Contour" piece but unless you have some major patience, its coming out in many pieces.
If you heat it up, the adhesive will relax a bit. It will still be a pain to get out though. Be sure to clean it with some alcohol after you get all the old adhesive off so the new tape will stick better.
As long as you don't scratch the outer black piece, it doesn't matter too much as the new carbon insert will cover anything up.
HTH
