Rubbing compound would help remove fin scratches if they were any. I don't think you would have much of a problem under a badge with that. Take some fishing line and slowly run it along the back of the badge to remove the adhesive. After you remove the badge gently role the adhesive using your thumb off the car. Clean of the remaining adhesive with paint safe bug and tar remover. Clay bay should remove most if not all of the remaining dirt/grime.