If so, this is probably yours because who else would drop their mouthguard on the corner of Bush and Montgomery streets and leave it there? We're guessing it was on your way to the dentist, or maybe you lost it en route home from getting your teeth/mouthguard professionally cleaned? If that's the case, it's probably not that dirty yet, and it's not like we found it in the Tenderloin.
Anyway, you should probably go claim it because grinding your teeth is a bitch and it annoys your bed mate. Also, unless you're shopping at Walgreen's, those things aren't cheap.