Looks like hair algae. You can use a toothbrush and wrap it up and remove it that way. Comes off relatively easy.
Kubla, I agree about some of the moss coming with the algae, but don't you agree, moss is so resilient that it will recover? Even if you trimmed it back to get rid the algae the moss will survive. That's my experience with moss because it is, for lack of a better term, invasive. At least for me, I've tried to get Christmas moss out of my tank completely for 2 years and I cannot because one little piece sticks in a crevice and grows and on and on so I just live with it.Hopefully someone will post with some ideas but I think you're going to have a tough time saving that moss. I've not had the experience of it coming of "relatively easy". I would expect it to hold on to the moss tighter than the moss holds itself together. Another words, you'll probably just tear the moss up trying manual toothbrush removal. H2O2 and excel that hurt the algae will also hurt the moss.