I believe you have to take the entire door apart to get those little wood trim pieces off. May be a bit more of a hassle than it is worth. If I may suggest, just tape off around the trim pieces on the door and throw a coat of primer on them and then a few coats of matte black paint. It wont be that carbon fiber look, but it will match the rest of your interior pretty well.
I had the same problem when I wrapped my wood trim and I opted to take the easy way out.