Yea, surface agitation will break up the surface tension of the water causing whatever particles that had built up on the surface to sink into the water. The filter should remove most of it.
Usually if you let water sit stagnate for a few days, you will begin to see a film develop on the surface. This is caused by the surface tension formed between the interface of water and air, formed by the bonding properties of the hydrogen in water molecules. This is where tiny organic materials and even micro-organisms (like bacteria) will accumulate. How often do you dust your furniture? I know in my house you can see a film of dust reaccumulate after a week. I suspect that's mostly what we see on the surface of a bucket of water after it's been sitting still for several days. However, in your turtle's tank, there's more than just dust that's accumulating.
That's how the protein skimmers that were previously mentioned operate. They force millions of almost microscopic air bubbles through a column of swirling water. Each air bubble is like a tiny ball of fly paper, catching any proteinaceous waste particles in the water column. As the bubble reaches the top of the column, it is pushed up into a narrower neck at the top of the column. This causes the bubbles to merge together into larger bubbles complete with all of the crud that they were able to catch on the way up. These larger bubbles rise up to the top of the neck which opens vertically into a collection cup. As the bubble is pushed up by the smaller bubbles underneath, it expands and eventually pops, spraying all the crud into the collection cup.
This works great in saltwater because the surface tension of saltwater is greather than that of freshwater. A protein skimmer will still work in freshwater but it will probably produce a wetter skimmate in the collection cup resulting in an increased need to add fresh water to the tank to make up for the water that is pulled out.
Hmmm, kind of like a continuous water change...I kind of like that idea!

I could take one of my old protein skimmers and hook it up to the turtle's tank. Then I could place a tub full of fresh water and hook it up to a float valve in the turtle's tank so as the level drops, fresh water is automatically added. This is what I do for my saltwater system to replace evaporated water (otherwise the saltwater would just keep getting "saltier" as the H2O evaporated. Well, I recently began modifying my old protein skimmer to turn it into a reverse flow phosphate reactor (to remove phosphates from the water) for the saltwater system. Maybe I'll put it back to its original configuration to try this expirement.
I'll post a new thread if/when i get this expirement started and let you know the results.