If you could get a close up picture of one with something like a penny beside or some reference of size there are probably people on this forum that could identify it.
It is likely a mussel if it is native to your area. Some mussels part of their life cycle is through the intestine of a bird so you may end up with them eventually.
On the other hand if it is an invasive species like zebra mussel you definitely do not want them in your pond.
Others on here are experts on aquatic plants so maybe they can help with transfer about how to avoid "hitch hiker" species.
An interesting side note on mussels. In Kansas all species of native mussel (and there are a lot of them) are protected. It is illegal to collect them alive or even the dead shells.
RES likely will control them till they get too big for the RES to crush or get in their mouth. I have 6" long mussels in my pond and have no idea how they got there or how they got so big so quick (in the first couple years after pond was built). Mussels
Oklahoma may have a similar resource. Life history of mussels