To decode the coding:
A5 = New York Yankees (also used for Highlanders players on early photos he reproduced)
C = copy (any photo taken by someone other than Burke that he reproduced, typically from a copy negative re-shot from an original photo or publication)
C-310 = (I presume) Germany Schaefer. Burke assigned a different number to every player whose photo he had on file. Schaefer's name does not appear on either of the catalog lists that I have, because he was no longer active when Burke began photographing players in 1929. (310 without the C is the player code he used for Jesse Haines). Burke had a separate catalog list of "Players of Yesterday" that he advertised, but I have never seen a surviving catalog list (if anyone ever runs across one, or the similar lists he had of American Association players, Groups of Players, or Players in Street Clothes, I would pay good money for them or even for clear scans).
The "Reproduced by Geo. Burke" stamping is typical for the stamping he used on photos that he did not shoot himself that he produced from copy negatives.
For what it's worth, if Burke put Herman Schaefer on the back, that's who he (or more likely, George Brace, who Burke hired for his baseball knowledge) thought it was. They weren't perfect on player ID's for those photos Burke didn't shoot himself, but they did seek out photos of those "old time" players who he never had a chance to shoot, in an attempt to compile a complete catalog of images of every major league player ever.
At a glance, Tillie Shafer does seem to be a better fit:
