Brian
We know for a fact that GOUDEY was still printing and issuing their 1933 cards as late as Nov / Dec 1933.
We know this because the bios on the backs of last 24 cards reflect the 1933 World Series (Giants vs. Washington).
Assuming that date on your Greenberg card is original, the original owner of that card simply forgot to advance the
year on his stamp. "July 1, 1934" would be an accurate date for when the 1934 Greenberg issued.
TED Z
T206 Reference
.