This is a type of macro algae and can be desirable (by some) I suspect its growth to lessen as time goes on. So my recommendation would be to give it time and see what happens, removing what appears to be excessive growth.
Does it look like this http://seaweed.ucg.ie/descriptions/Delsan.html or this http://seaweed.ucg.ie/descriptions/Phyrub.html
Im sure its closely related to this family. Macroalgaes are good for a tank as they will uptake nitrate there by reducing your nitrate levels. The macroalgae will only populate to its conditions, which *could* be why you don't have any nitrate reading. If you are concerned about phosphates or silicates... this shouldn't be a problem if you use ro or di water.
On the other hand *if* you don't have hair algae your water is probably fine. So I would cultivate the plants as they are desirable and will produce a more natural setting, pruning of course as needed. Search the links I gave you and you may find the exact species.