From reefcleaners.org
Caulerpa Racemosa, Grape Caulerpa
Caulerpa racemosa has perhaps single handedly given Caulerpa spp. a bad name. Highly variable, it can be generally described as a grape like plant that grows up from a runner, (or root system). While other species of caulerpa may appear different, their treatment is generally the same:
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.
Why it happened - You didn't quarantine, and you have available nutrients for it. Try to keep it out of your tank, and if it happens to make its way in anyway try to get it out before it can spread.
Starving it out - Use a phosban reactor or a macro like chaeto to take down phosphate. If you have a nitrate problem too, you can add more live rock or rubble to the tank, do some more wcs, add macro, add dsb, etc...
Caulerpa racemosa in all its forms is invasive. Its runner is too fragile to practically prune and it can be a frustrating problem. If you like the look of grape caulerpa, try Caulerpa cupressoides var. lycopodium. It carries the same risks as other caulerpas, but its strong sturdy holdfast makes pruning easy.