a guy named ray, who created a specific method of growing plants using the clay pellets (he calls it semi-hydroponics) advocates the use of physan-20.

you might also try bleach or a dishwasher

I did try the dish soap thing, diluted and tried to swish it around, but it didnt work. Thanks for the tip, I will look for the physan.

I do lots of water cuttings, & don't change the water, I just add to it. I use aquariumn grade charcoal (small chips), I toss a few chips in the cuttings water & I don't get algae nor does the water get yucky.

I can't suggest how to clean up the current mess (except very gently tease the roots off the clay balls if that's possible). But perhaps by using the charcoal in the future you can prevent the whole problem.

I grow some small Hoyas in leca stones (turface?) clay balls (?) & water, I use a bit of charcoal in there too.

A mild houseplant fungicide (diluted according to directions) might help.

I usually use bleach or vinegar to kill algae. Use a damp cloth with vinegar on it to wipe the algae off the glass, then wash the LECA with bleach to kill the algae, leave the attached bits to the roots, rinse everything then put about half a cup/2 lb LECA mixed together around the roots. I like to mix them because I don't really like the layered look, but you can do that also.

Years ago when I had aquariums the fish people sold anti-algae stuff. I don't recall what it was. Other water plants in the aquarium were not affected as I recall.

The problem with the anti-algae stuff is it causes an imbalance of nutrients which could harm the plants eventually. It makes an influx of amonia/ammonium, which feeds the plants, however too much causes quick, weak growth which never really recovers. If the amonia/ammonium level gets too high the plant will shut down until the level gets to a more managable stage, (water changes). Besides, unless the algae is removed, it will come back in droves.

Algae is an indicator that there is something wrong with the lighting and/or nutrient level, both of which should be remodied, before adding more chemicals to the water.

I forgot to add in my previous post decaying plant matter will cause algae to grow, so be sure to check the roots for breakage and unhealthy brown or mushy growth and trim them to healthy white growth, and keep any dead leaves from falling in the water.