A sea urchin or perhaps removing the rock and using a wire brush is probably your best bet. Make sure to do this in a bucket of saltwater though. This way you'll be able to save the beneficial bacteria on/within the rock along with any micro fauna that has decided to make it their home.
Hydrogen Peroxide is something you might want to look into as well. Sometimes this is used to combat certain types of algae. GL.
if I had one of those planted reef tanks like metrokat, the kind with reds and purple plant focus I'd specifically want that green you have above as a putting green carpet
Use trimmers to keep it down, don't rob it of phosphates and feed use precision aquascaping trimmers from online that is a neat plant for some tanks
if it misbehaves, we can lift out any noncompliants then access some 3% and hit it outside the tank easily, scape it off outside the tank for easy catch up.
Take the rock out of the tank during a water change, scrub, rinse, add some hydrogen peroxide and let it soak 10-15 mins. Use food grade 35% and dilute it down. The brown bottle peroxides at Walmart, etc, have stabilizers that are toxic.
Otherwise look at the Red Sea program, nopox does wonders for long term management.