========== From Julian Sprung =========
Dear Steve,
That's Pseudolithoderma, which used to be known as Ralfsia. See page 54 in my book Algae: A Problem Solver Guide. It is a brown seaweed that adheres tightly to rock and other solid surfaces. The filaments are a sign that it is growning and healthy. This is, in my opinion, as desirable alga, quite like various coralline algae. A strong growth of it usually indicates good water quality. I can't imagine why you would want to remove it!
If you wanted to curb its growth and encourage more diversity of corallines, you might try adding one Diadema urchin. Otherwise leave it alone.
Sincerely,
Julian Sprung