Because I almost never make a guess in this forum, I'm replying mainly to give Nhbenz a public round of applause for finding an EXACT match for that emblem... including not only the very same unusual letter-font of the "H," and the letter's border, but also the very-unusual shield's shape, and even the shield's double-border. It seems much too exact to be coincidental.
I agree that the two "outer" marks on the object's back are from an injection-molding process in manufacturing it. I suspect the central mark is where a screw-pin or clutch-pin was attached (now broken off). Although that mark may have been where a button's thread-loop was attached, I agree that the object (at 1/4-inch thick) is too thick to be a button. So, in summary, I think it was a Harry Potter souvenir badge/pin -- or perhaps, a "decoration" on some other Harry Potter souvenir. I may be incorrect about it being a pin or decoration -- but as I said, the match-up with the Hogwarts Shield logo seems too exact to be mere coincidence.