Sounds like feather Caulerpa, but could be something else, too.....two ways I can think of to get rid of it would be to keep ripping it out, or get a tang to eat it. Not knowing the size or other inhabitants of your tank i can't speculate on whether the tang option would work for you.
Caulerpa is a great nutrient sponge. If you have a refugium you could try and grow some in there. If you do decide to get rid of it, try bringing it to a local LFS
for store credit.