Intex pool filters are too small to clean up dead algae . . . in your lifetime.

It *can* be done. The fastest way is probably to kill the algae, turn off the pump and let it settle, and then vacuum it out to waste.

In your case, adding liquid chlorine (just strong bleach!!) was fine. Adding "mustard algae killer"? Not so much. Was it an ammonia based, or bromide based product? (Either way, there are long term negative consequences.)

You may want to look at the cost of draining and refilling. If it's less than $60 or $70, that's what I'd recommend. Then, use the SS recipe (link in my blue signature block) when you restart.