Grass maybe.

I think rock mulch is better and then plant anything to hide the rock if you like. If you can dig down the dirt and replace with rock. Plants can go up thru a thick layer of rock mulch.

Any kind of thick ground cover - not sure what grows well in your area - will do the trick. We have vinca along one edge of our pond that is low to keep the much out of the pond. As it fills in it does a great job.

Ground cover is great for stopping splash from rain, but for water running down over soil and into the pond I would think a more dense stem system would be more helpful. But the dirt in the pond could be from rain splash and not running water, unless you're seeing actual eroded soil.

Go to the dollar store and buy a cheap polyester blanket - brown or sand colored is good. Cut it in strips as wide as needed. Cover your banks with it and tuck the bottom edge under/behind the pond liner. Cover it with rocks, gravel, and cut a few small planting holes as needed. Creeping Jenny and some grasses will grow right over and thru it. Sherry

ah good to know, ty

Zee,
Liriope, daylillies, variegated ornamental grass, a dwarf variety, and japanese iris (it gets tall), but the japanese iris is awesome with guarding a pond edge from anything.