I've sanded carbon and still been able to clear coat afterwards with really good results. Granted, you don't want to go crazy sanding into the carbon but you can take off a bit and refinish to a really nice finish.

In this case, I would try some sort of stripper first - but if they used Imron or similar, you're going to have a really tough time getting it off - and I have no idea what strippers might do with the epoxy in the laminate.