Ive found even after taking the wood out the tank, leaving it for months and then re adding the algae just seems to survive. Best option would be removing and literally rub it off, it still may come back..often it does.
The main part would be finding the source of algae growth aswell and that will maximise the chances of it not coming back
when i bought my first fish tank a small 12x10x10 it came with a smal piece of bogwood and it was very dark and on closer inspection i saw it was dried hair algae. the person who sold us it had told us the tank had been left by a couple who she had rented a house out to and the tank had been sat empty and broken down for months. i rinsed off the wood before putting it into the tank when we'd set it all up and it almost instantly it all came back to life. it must have been sat dry for aorund a good 4 months
i wouldnt be too worried about your algae. i cant see any and not sure where im supposed to be looking. lol i'll have to show you my piece of bogwood now. you'll be amazed