Algae on Birdsnest

So I rescued a beautiful little birdsnest from the LFS.. Recently their little frag eggcrate shelf was knocked over and their corals fell over. Well this birdsnest looked really sad today. It had hair algae growing on some of the tips. I tried my best to pick off the algae, however it's not all coming off. Where the algae has taken over there's no more polyps. Over 80% of the colony is fine so in case it starts RTNing I can rescue some of it.

Should I take tweezers and try to get every last little algae strand off the branches? The coral has two large trunks that go up, and a number of branches off the two. One of the two is the one with algae. It also had some growing in the crease between the branches with a good 2" between the algae "colonies". It had really nice polyp extension about 1 hour after introduction.
 
Yes, I would clean away any algae you can. And perhaps put some snails nearby to munch off the rest of it.
 
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