The mesh and red band are one piece. They're usually attached by heat shrinking them on (maybe with a little adhesive too). They're not necessary to attach the leader to the fly line, in fact I think far more people DON'T use them than DO. It's very unlikely that loop will break unless it gets cut somehow. Your knots are going to break much sooner.
If you find that you don't like it for some reason, you can carefully cut it off with a razor blade. If you can't cut it off, you can cut off that short portion of the fly line (which shouldn't affect the line's characteristics a noticeable amount).
My passion for catching fish is eclipsed only by the fish's passion not to be caught.