Your description does sound like a Caulerpa specie. I have not had a plant like the one in ClamIam's avatar in my system. However, I can speak generally about controlling creeping, fragile specie of Caulerpa.
Harvesting Caulerpa in-tank is problematic. Caulerpa spreads readily by fragmentation. You can harvest while siphoning out water with a hose held near where you are ripping out the Caulerpa to try and catch the fragments. If you don't want to replace all of that water, run it through a filter sock to catch the fragments. A better method, if possible, is to remove the rock from the tank and wire brush it. Rinse the remnants off of the rock before returning it to the tank. Using a pressure washer might be more effective if there is nothing on the rock you wouldn't mind loosing.
Since this Caulerpa is so fragile, it may be grazed by a pygmy angelfish, which would 'fit' in a 55gal. A rabbitfish like Siganus would be more likely to graze it, IMO, but evn the smaller foxface rabbitfish grows into a fairly large fish. I have not found an urchin that will preferentially graze Caulerpa, and there are Caulerpas that even macho urchins like Diadema will avoid. There are sea slugs specialized to graze on siphonous green algae. Some of these sea slugs have short life spans and do not graze during their whole life span. The best known one is the lettuce sea slug, but other slugs sold as "sea bunnies" and "sea hares" are making their way into the hobby. Of these, I have tried the lettuce sea slug and was not impressed - probably collected after the slug had stopped grazing.
Given that is a brand new tank, I would try pressure washing the rock, myself, to rid it of Caulerpa. After there is a lot of encrusted coral, this will not be an option.
