From Reefcleaners.org
Manual Removal -If you are going to manually remove it, use a dental pick to make sure you get every last bit of runner removed. The thicker the runner on your variation of caulerpa the easier this will be.
Clean Up Crew- Emerald Crabs, Sea Hares, Tangs, Angels, Urchins, some Turbos, Chitons, Limpets, and the Longnose Decorator Crab will all eat it this and other species of Caulerpa.