A, according to the label, the lining is polyester, so A is correct;

B, polyester is a synthetic material, belonging to organic polymer materials, so B is correct;

C, polyester is a synthetic material, not a natural fiber, so C is wrong;

D. Polyester is a synthetic material, and it doesn't smell of burnt feathers when burning, while the main component of wool is protein, which smells of burnt feathers when burning, so it can be used to distinguish polyester from wool, so D is correct.

So choose C.