The muck is all the algae that was making the water green. Single algae cells clump together, called colonies, to try and protect themselves from UV, normally UV from the sun. That makes them heavier and they sink. This all works very much like dust in the house. A lot settles, some is always suspended.

There's no requirement to remove this stuff, but there's no benefit either. In high fish load ponds people don't want it because it consumes O2 as it decays and produces stuff that degrade water quality. A normal Water Garden fish load can handle that no problem and you have a lot of moving water so even less of a problem.

People who have a Wildlife Pond like the stuff because insects live in it creating a food chain. That's good for dragonfly and damselfly larvae.

The downside is how it looks. Longer term, as it decays it becomes smaller and smaller bits and at a certain size it's called DOC (dissolved organic carbon/compounds). The reason a name is given to that size is because it acts differently, acts like soap, can create foam on the water surface. As it continues to decay it gets even smaller (we're talking the size of bacteria) and it stops being a DOC.

Another issue is as it decays it becomes lighter and over time (like a year or two) it starts to not settle back down and becomes suspended. Looks like pale ground pepper suspended in the water. That makes the water less clear, and just generally dirty. There are filters that can deal with that but it a bit tricky.

There was a time when I just let it be. But I changed to removing it and keeping the pond clean. Just made keeping the pond easier, water clearer.

It can be removed with a fine net, like those green minnow nets from the pet store. You have to scoop very slow.

I use a vacuum I make that I call a Silt Vac
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In a small pond the net works very good. Your size pond is kind of in the middle, kind of too big for a net, kind of small for a vacuum. But the Silt Vac can certainly be scaled down and a smaller pump used.

I also have a web page that compares the different kinds of vacuums. Really important to pick the right vac for the pond size and also what you're removing. For this fine stuff you need a vac that removes water. Trying to filter the water to return it is a real waste of time...tried many ways.

Loose gravel makes vacuuming difficult. You can put a valve on the pump to reduce power and try to get the sweet spot where there's not enough power to lift gravel, but that slows you down too.

I like rocks on the bottom but I like them mortared. That makes vacuuming really easy, even better than bare liner because no wrinkles and the rocks look nice when clean so it's a reward where seeing bare liner isn't so nice imo.
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If you do decide to vacuum it's nice to have a place to hook the hose to so you don't have to have a separate pump. This is how swimming pools are built, the skimmer has an intake that is sized for the hoses and the pump just sucks the hose into place. Very easy. Unlike a swimming pool though you need valve(s) so the pump exit goes into the yard. I used a separate pump because I cleaned other peoples ponds.

This settling stuff will normally be on on going thing, just like dust in the house.

There are ways to direct pump output to the bottom to keep the stuff from settling so filters can remove it. But that is more complex than it sounds. Your filter for example will remove some of this stuff but probably only maybe 10-20%. There are other filters that remove more. It's a whole deal.

Wow, I can't thank you enough for your response. I've bookmarked it and have gone back to reference it a couple of times this week. My pond is just vinyl on the bottom - no rocks. We don't even have much in the way of trees in our yard, just around it. So not really much in the way of debris, either. I ordered a muck vac - not the really nice ones, but the $70 one that uses suction from the garden hose to suck the bad water out the outlet hose. We'll see how it goes! I've added a few floating islands with plants hanging bare root in the water. I'm hoping they will grow (I can't seem to get water lettuce or water hyacinth or even duckweed to take off in my pond).

Thanks again for all of the information - your post is the only information I've found that clarifies the problem I've been having. This might be the season I am able to see the bottom!

You are welcome.

Some people like the Muck-Vac, many don't. Partly it's because city water pressure varies. Partly it's expectation, you have to go slower than some people like. Partly it's pond size, cleaning a 10,000 gal pond with a Mick-Vac would be no fun.

Partly it's what's in the pond, lots of things clog it. I would never even bother starting with a Silt Vac, always started with the Muck Mop. No matter how little big stuff appeared to be down there it always seemed to be enough to clog the "remove water" vacs.

So if you aren't happy with the Muck-Vac I would return it right away.

If the water temp is good and you still can't get water lettuce, water hyacinth and duckweed to grow try growing it in a separate container (5 gal bucket, whatever) with no fish. Goldfish and Koi can nibble new roots on WL and WH so they don't grow hardly at all and slowly die. Duckweed is a fav food of some fish. Fish are funny. Some eat this stuff, some don't. The better fed the fish the less likely.

Putting some in another container just tells you if that is the problem. Plus often, once the WL/WH has a big root system they seem to be OK with the fish. But I assume that depends on the fish.

The plants you mention aren't thriving because your pond is in full sun. The fish are eating your duckweed as fast as it proliferates. I'd suggest adding some lilies and a few perennial aquatics that prefer full sun for some coverage. Get your plant (surface area) to fish ratio balanced and your pond will clear up in time.