Plucking won't solve the issue. I have had hair algae issues on and off and they're caused generally by 2 things: too much light, or too much/little nutrients (not to be confused with ferts). In my case, one tank has developed it because it's receiving light around 12 hours+ per day (it's next to where my seeding plants are, and those have a light on 12 hours per day). I'd limit your light to around 8 hours a day; if you're at a window, less. After that, ensure you aren't overfeeding your beta.
You can also remove it, as mentioned, but that's just going to grow back if you don't get to the root cause.
I'm having a similar problem at the mo with hair algae (since changing out CO2) - but it doesn't look like this (mine is fine and readily floats in the current) - this looks more like staghorn except there's rather a lot of it!. You also have some brown algae - how well established is your tank? It may be your going through one of the stages of 'new tank' syndrome and just need to let things settle.