No, it's not simply "give this group x permission", especially when it comes to assigning and removing server groups.
Allowing access to rewards would allow GMMs access to any teamspeak award tags, and I have no idea who GMMs are or anything to do with them, contact an HA+ for tags like any other weekly award.
Also, let's just say my experience with the GM team has been subpar at best and I wouldn't trust you with anymore perms than you already have.