That "algae" is a PITA to deal with but loves nutrient rich environments with lower current with low oxygen. It can also use light that other plants do not like so having proper lighting that works better for plants to help out compete for the nutrients.
This in your tank, what size, filter, etc?
I would: Clean and do partial water changes, add current and air. Clean again in 3-7 days.
I wouldn't: Add hydrogen peroxide to it, but maybe clean off decor with it.
Also keep in mind, killing it in the tank, will add more nutrients to help feed it.