to sum up headache's worth of reading to find your specific invader among those listed, its this:
take out an easy to reach test rock that doesn't destruct your whole set, and remove it from the tank. use a metal tool or knife to literally rasp and remove 100% of it off. That rock is now carpet free. toothbrushing wont work, that leaves holdfasts/roots. knife or metal tool doesn't, you just made your test rock free of brush algae like a parrotfish would have done on the real reef (now we begin to match the natural complements of control to a specific invader, an anchored benthic variant) and the scrapes you made will seat back over with coralline in time.
put peroxide on the cleaned areas now, let sit for 4 mins cooking the microscopic bits you missed.
put rock back in, and now compare it to all other methods you will ever try and see which is best and post us before and after pics.
any other method you'll try is a whole tank commitment + time + variability in outcome, the threads will show for it.
any test rock you do with our method has no variability and only has fixed results though they are buried among a bunch of verbose type heh. check the threads, pix galore. To have a brush algae problem past tomorrow is fully optional choice, talk about a stated compliance date...