Yeah, it's a Police Sports Badge. Thank you all for your information. I know that my grandpa brought it back from WWII so it's legit. It looks like it was cut off of the shirt with a knife or just torn off. Either way, it's pretty cool, other than the link to what those bastards did. My brother told me that there are supposed to be other "souvenirs" in a box that we've yet to find. Can't wait to find it and see what grandpa brought back.
Most of my grandpa's "souvenirs" went way before I came along. As I understand it, he brought back a P. 38, a Mauser with a bayonet, and a Nazi canteen. The canteen was covered in grey felt, with a red, white and black felt swastika on it. It was given to the soldier by someone, but the writing is obscured with blood.
The story is that grandpa lost his rifle seeking cover during a mortar attack, landed in a foxhole with a German who was doing the same, and managed to grab the guys rifle and bash his teeth in with it. He left the foxhole with an enemy rifle and his water supply.
The Mauser was traded for beer in the '50s. The P. 38 was traded for work of some kind. The bayonet was used as a pry bar at one point, broken, and then ground into a knife. It's in one of my dad's tool boxes. The canteen is in my dad's gun safe.