TLDR: If I were you, I wouldn't worry about it not coming out on initial removal. Just make sure you get it suspended if you have dead spots, and get one of those in tank micron filters to help create flow and suck up the junk. Makes the job 10s of times easier.
I went on a vacation and then came back to not notice neglect my tank a little around november december last year, and before I realized it I had 2 inch thick bubble algae on all the rock away from the front display, it grew so fast from that point that it would cover the overflow and pumps overnight and was kind of hard to scrape away.
I did the dumb thing and decided like all other pest algaes I had was to just continue what I was doing and it would die off since I had crabs to eat it. Good lord I was wrong, the baseball size chunks were just breaking off on their own and regrowing in no time. The move I did to get rid of it was get one of those marineland in tank magnum polishing filters, and just bust the stuff up. I didn't worry about getting it out of the tank, just getting it detached.
it took a week of a stiff tooth brush and bashing on it just to pop it and free it from surfaces. it seemed that microbacter razor I started dosing at the end of this, that the bubble algae couldn't even hold on anymore and would just get knocked loose by flow. in total, I went from probably a volume of 10 gallons of bubble algae to none with only a few hours of work.
The poor decisions that led me to this was primarily the never having measurable nutrients, I was heavily dosing ammonium and nitrates and phosphate to keep it up, but soon as I went on vacation and stopped, and stopped dosing chaeto grow, the nutrients shifted from my healthy chaeto to the ugly bubbles. and I decided the new normal of not dosing these things was what I should continue to let the tank stabilize. In the future, if I see a patch of it spreading, I will absolutely put the filter back in the display and bash and scrub it out.