My reef has been up and running for a little over 3 months. I had a lot of HA growing in my overflow box that I scrapped out. Some of it made it back to the display tank where a HA bloom has taken off. I think it is living off the nutrients in the rock. How long does this stuff take to burn off. I'm going to beef up the snail side of my CUC.
What is your reason to suspect the rock?
Typically algae like this is from stocking the tank too fast and maybe too much as well (with the commensurate feeding to match). Leave your critters hungry after every feeding, and usually feeding every other day or less is recommended. (There are a few exceptions.)
Lighting of 6 hours per day or less would be recommended, 4 as a regular minimum. One to three days of darkness can help dent the algae without stressing coral much/at all.
More nutrient removal is also needed - CUC does not help much with this, just with keeping new growth down.
More/bigger water changes.
Manually removing as much hair every day as possible (toothbrush+siphon hose are a proven combo). At least every day that you can see new growth.
If you don't run a skimmer, start. If you aren't cleaning it every day or close, start. If you aren't wet skimming, start.

A little carbon and phosphate media will help once you get the algae on the decline - don't over-do it.
-Matt