you can do anything with the CF,...
u can sand it down,... thinner should be quite risky, later melt the epoxy haha,...
one thing you can see after the paint layer is being removed,... whether the CF is "cooked" or not,... meaning some patchy different tone everywhere,...
if cooked,... you continue sand until nipis also no use,...
and you are not able to lacquer the CF,... it wont stick long,... at least mine acted that way,...
lacquer and the CF epoxy have different expansion/contraction/shrinkage,... so they will divorce in say,.. a week or two. Unless some paintguy can come out with someting that make those two material bond/kahwin/etc,... then nothing can save it.
if you sand it down, and get a good tone and uniformed tone,... just leave it like that.
another option,... install the CF lookalike "cloth" sticker,...
i still prefer the original CF clear (3d look,... fibre cloth visible in between the epoxy), but if no choice,... wat to do,..???
else, paint it the color or your car, but make sure the paint also good type, can bond/kahwin, or else your paint layer later also peel off,...