Looks more like a rank insignia on the cover, not an emblem. I’d suggest Navy.
The covers on backwards to allow the face shield (blue strap). It’s either a globe/anchor or a 1st/2nd class petty officer’s eagle and chevrons, but I can’t ever remember navy MPs in that getup.
I thought the Marines ran that particular compound, but there’s plenty of navy on Gitmo, so I could see supplemental coming from there and a common uniform required.