If you are only seeing this in the toilet tanks, clean them more frequently and don't worry about it because it isn't harming anything.
Yes it could be from the pump stirring up sediment in the well but it could also be from ferrous iron content in your water and it converting to ferric iron in the water in the toilet tank, falling to the bottom of the tank. Either way it is harmless and not worth worrying about.
And you should never throw anything down a well, especially with a pump in the well. Wells can be cleaned or you can raise the pump 5'-10'.