Green’s Dictionary of Slang

fitch n.

[SE fitch, the hair of a polecat]

(US Und.) fur, as worn in a coat.

[US](con. 1920s) ‘Harry Grey’ Hoods (1953) 108: She was covered in furs and blazing diamonds [...] Cockeye ran all around her [...] ‘You look like a classy bitch in all that fitch.’.