Yeah, colonial tunicates - typically, you should be able to just scrape these off pretty easily (generally speaking, with exceptions for food specialists like nudibranchs that would be all but impossible to obtain, anything that might eat these might eat corals too).
As you have found, some colonial tunicates can spread pretty invasively, but tunicates are filter feeders, and most tunicates are harmless. Some tunicates may chemically combat corals for space to grow on the rocks - and this might explain your unhappy corals - but I'd personally look for other possible explanations for why your corals are unhappy just to be safe (if for no other reason than the fact that chemically offensive tunicates are rare).
