I would definitely recommend adding something to help. But chemi clean has mixed results and alot of water changes involved. It would probably work and be fairly harmless since it doesn't look like you have any coral. I had an unbelievable bubble algae/ cyno infestation not that long ago. I tried it all. Peroxide, chemi clean, 0 light for 48 hours. I nearly killed every coral in my tank! The only thing that survived well...You guessed it, Bubble algae! I had almost given up until I decided to try that new "Vibrant" bacteria additive I heard about on this site. I broke the dose down to twice a week and just did normal water changes and within a couple of weeks huge chunks of bubble A. We're breaking off and getting hung up in my power heads.( which became a bit of a nuisance on it's own) but the bubble a. was done! The only down side I would even mention and only Bc I see you have cheato in your refugium. I had alot of cheato also. (Which clearly didn't fight my algae problem very well) and it seriously receded. It didn't die. It just shrunk. So I removed it and added lbs of rock instead. It gave more surface area for the bacteria to grow. My nutrients, Na ,Po have been 0 now. My protien skimmer barley produces anything. I'm actually having problems with my LPS and softies because my nutrients are to low. I have to target feed now. I would definitely give Vibrant a try first. And as always, patients is definitely key in this hobby. Good luck.