Maybe not a W575, maybe not a D383, but how about an E?

[nolemmings]

That same message can be found on the backs of American Caramel E123 Actors & Actresses, which more closely aligns with the issuance date of the Koester cards than does E124 (which were supposedly issued in 1923 per Google). I don't collect non-sports, and there seems to be a disagreement as to when E123s were first issued--Google has articles/ads for them represented as 1920, 1921 or 1922. The fronts of these actress cards are patterned after the ornate-framed E120s and not the square-framed e121s. They also have a blank-backed counterpart, W585, which could have been stamped.

It seems your card has a Koester's only subject, which dates it to late 1921. So it seems to line up with E123/W585. I’m having trouble picturing how a confectionery company employee stamping the backs of piles of W585s would somehow accidentally stamp a baseball card laying around. Maybe the same company also was privy to the Koester cards and had a separate stamp for those? Anyway, it would seem that the company would likely be located in the NYC area where Koester’s were distributed.