This is dead and decomposing algae. It was suspended algae (single cell) that clumps together and remains green for a long time. The clumps become so large they sink. It remains green for a long time. Single cell algae clumps (called colonies) to try and protect itself from the sun's UV rays.
Couple of options for removal.
A very, very fine filter. Or a filter that can be clogged, like quilt batting, but water flow must be slow enough that the batting isn't "cleaned" by the flow. A bit tricky. Or a sand & gravel filter.
A much easier fix is to
vacuum it out using. You have to
use a vacuum that removes water from the pond along with the settled algae. There are some vacs sold that do this but also use a bag to filter the water so it can go back into the pond. These are not good. Better to use the waste water for the landscape and replace the water with new water.
Or just wait. Over time this algae will continue to die and decompose. However the process is likely to continue with new algae being created, clumping and settling. And in most ponds the build up is faster than the decaying so waiting doesn't really work.
And the decaying creates some issues. The dead bodies go back into suspension and over time make the water less clear. Looks like dust in the water. As it decays further the bits become DOCs which can create a foam on the water surface.
This type of algae is also not a very good algae. It's at the end of its life cycle and not reproducing very fast so not consuming ammonia as much. The settling blankets good algae and bacteria which can reduce their benefits. And of course the entire decaying process is not good for fish. Bigger the fish load the bigger the issue. However, in most Water Gardens it certainly isn't the end of the world. But if you don't like the look, or the possible problems down the road, I'd remove it.
