They will mow it down for you, but you need to get to the root of the issue to stop it from continuing. Increase your water changes and change out more frequently- or add- a GFO type product if you aren't currently running any.
keep PO4 and Nitrate down by weekly water change (instead of 10% or 15% do 20%. ) less feeding, little less light and run GFO.
I use to have green hair algea and fight with it for 2 months with water change and GFO to keep PO4 to zero. it gone by 2 months. you can also add CHITON. they eat green hair algea as well.