the ideal way to handle this algae is to make a single test rock comply as algae free and not the whole tank. your grazers like it and its not ugly, its in balance as it should be. it is an invasive variant its your grazers keeping it in check, as they should. good balance.
you need to have the ability to command the tank free of it though, we've covered prob 10+ tanks with before and after pics of this algae in the peroxide threads and regular peroxide doesn't work well on it, it likes 35% which is more work to come by and signifies strong invasion potential as 3% w beat most invaders.
If you find that no matter what you do you cant keep 1 single rock totally free of it, then start large scale tank work and switch tangs to alts
the way I would beat it is w 3% first, use metal tool to scrape it out of all corners first, all external work outside the tank so things can rinse clear, only physical actions like a dentist would use on plaque. apply 3% to all scraped surfaces as clean up, rinse, install rock see if it grows back. if the test rock grows back, take a meaner action and document for us what it takes to consistently keep 1 rock free of it.
If one rock worked over just once stays free n clear for months, then sit back and enjoy the natural feed balance, rather rare...low potential invasion is revealed in that kind of test rock response.