Hey Bro.
I searched around and found a site with the described badge. The same design was listed as Scottish rite and Masonic crest interchangeably. I'm not Scottish Rite but those friends of mine who are would never suffer the "lower case" R in Rite. Sounds like an uninformed copywriter. The badge is pretty straight-up Blue Lodge stuff. I'm unfamiliar with the oak leaves but that doesn't worry me too much. I'd say go ahead and wear it (in all 51 jurisdictions) and if some purist howls at you for a faux pas, use it as an excuse to go through Scottish Rite.
Bob
KB1 LEL