Looks like some type of cyanobacteria. You can try manually removing it, but I find it's best to let it grow to the point where it stops growing and then remove as much as possible. By this point, it's used up most of the nutrients and I've never had it grow back.
Looks to me like something that was on the rock before you got it.
What kind of rock?
Manual removal and removal by a fish or something in the tank may be the best way to go. It is not a normal hair algae problem.
Reducing nutrients may or may not help something like that, but it likely won't hurt and I'd try it. I'd probably use GFO (iron based phosphate binder).