no don't do it that way
take out the specimen like its a big tooth, the flesh is the gumline
using metal, not a brush, a knife or an actual dentist's rasp, be the dentist: you carefully scrape pick and debride off all the attachments you dont want from the skeleton, damaging the skeleton just a little to hit the anchor cells.
once it's fully clean, then you paint on peroxide only on the skeletal part (the tooth) and let it sit several minutes then put back in the tank. expect to repeat a few times, peroxide should never touch the polyp/no algae grows there.
this action is reef dentistry and will work completely in 1-3 passes depending on cross contamination of algae fragments from other areas in the tank.
if you do it the planned way it just stresses the polyp and grows back over and over. truly debriding it off the anchor points is the right way.