Oops, you put a koi in a lake?

Don't tell any of your neighbors, koi are usually invasive species, and not allowed to be put into any natural waterways. Don't worry, we won't tell!
Welcome GardenLady I just read your post. In the beginning while reading it, I wondered if possibly you had a leak in your bog possibly, thus the muddy water. Did you by any chance look REALLY CLOSELY when you emptied your pond? I had a leak this spring in my bog, had to unload all the pea gravel ... twice ... before I finally found the leak. My leak was at the bottom, and draining toward the yard, but if you have a leak on the pond side, could it possibly be draining toward the pond? I think there is likely 2 layers of liner between the bog and the pond, but just a thought for the brown water.
Also, any type of wood close to the water that could be leaching brown tanins into the water?
Green water, it's fine to leave it, and it will clear up on it's own. The pond person probably was right about it would have been better to deal with what you had, rather than draining your pond. What happens (and I'm no expert, just my second year, learning as I go) is that when you replace all the water, you are literally starting all over. All the good bacterial that you had built up over the years was mostly gone, except what you had in your bog. And, if you pulled all the plants out of your bog, did the loosened dirt drain over into the pond, too? Again, this year when I planted a new bog in a new pond, I had issues with murky water, what you might have called muddy, as it was not pea green, it was brown. I added water when the level went down, drained about 10% of it and refreshed it, but no more than 10% at a time. Plants took a while to root, and once they started actively growing, things cleared up pronto. With the new plants, they will take a while to start using the nutrients, and then they will help clear up the water.
Another question: Do you have pea gravel in your bog or dirt? Some have a little of both, others all pea gravel. I know the muddy water came before you cleared out your old plants, but again wondering if the bog had something to do with the muddy water.
Whatever it takes, try to be patient and wait it out. The water looks greenish, so I assume pea soup algae, but that will clear up with some patience. A product I used and not positive it helped, but the pond did finally cycle long enough that it cleared up, and I have to hope that the beneficial bacteria product Pond Perfect helped get the bacteria going. I would not use any products made for clearing up your pond, unless they are products to add beneficial bacteria. The quilt batting will help the suspended stuff in the water column. If you have your water pumping through a pea gravel bog, up through the gravel, that should be filtering most of the particles as well, and feeding them to the plants.
As we all hope, good luck with your water. It will clear up in time, be patient, give it more plants to use up the nutrients, and things will balance out. Not sure what set it off this year when it's been so good for so many years, but more typical is that a pond "turns" spring and fall, and sounds like yours has always remained consistent, and this year decided to turn over.
