Dave N.,
While Baker may not have used the "C" designation in their catalogs, they did use it in their ledger sheets as found in the records. They also had a few other grades listed which I have never seen. The model 1897 was called either a "D" or "T" grade depending on the barrel type, damascus vs twist.
Baker marketed these guns through a number of venues with many different names encounted; New Era, Tryon, Imperial, Able, Montgomery Wards, Rec-O-Vac, etc.
Chris