A couple of possibilities include these:

BATEY, T. M., Co. “E”
BOWLES, T. M., Co. “A”

(I'm assuming, of course, that "B" is the surname initial. Suppose it could be "T., M. B.")

There are also several men with the last name, "B...." and a first name, "T...." whose middle initial I don't know.

Is there a context for this set of initials?