Hmmmmm ... "Fake" in the context of these badges would have to mean "non period". On the basis that everybody and their uncle would have cashed in on the Olympics, the controls associated with the manufacture of souvenirs would, I imagine, have been a lot less rigorous than say for the Reichszeugmeisterei (RZM) and NSDAP items. I'm not going to be as bold as to say that it's categorically not a fake (i.e. a later creation), however it presses most buttons for me. PS While I can understand why the use of the swastika on trinkets and souvenirs would have been discouraged by the Olympic committee, I imagine the Nazi hierarchy took a diometrically opposite view given the politics behind staging the Olympics in Germany at that time.