I have no idea whether that was complimentary or not but I suspect it was not. Probably just the normal competition between services WW2-style. I haven't heard the term used in decades but it might still be lurking out there somewhere.
Having served in the Navy in WW2, you are right when you say we called them Gyreens. I have no idea why. However I never thought of it as a put down. If we were going to poke fun we would call them Bell Hops or yell "telegram".
Of course it was all in fun and they called us "mop heads" and othe things. I served aboard an amphib ship and we hauled both army and marines. They all seemed great to me. We even hauled Australian troops in an invasion of Borneo. Its all the same when you hit the beach. The enemy don't give a hoot what your are.