That's obviously an isolated incident...either manufacturer defect led to premature peeling of the clear coat or owner neglect. Either way, that clear would need to be stripped down and resprayed. The CF underneath looks fine.
You have nothing to worry about. Clean it, polish, wax, just as you would with a metal roof.
2016 Individual F80 M3 - San Marino Blue|Full Amaro | Built by IMG Motorsport and Prime Performance | Mode Carbon | ESS | Akrapovic EVO | KW HAS | M Performance...
2012 MR e92 M3 DCT, fully loaded... GONE but not forgotten!
2008 e92 M3 Coupe 6MT | AW/BLK Extended...SOLD!