I have no idea what those parts are or from.
When you say "cylinder" I suspect you mean the resin tank. If so the parts couldn't have gotten up into the valve or cause problems unless they got down to the bottom basket and even then, that would maybe reduce a teeny tiny bit of water flow but that's it.
There are other causes of a 5600 jamming and usually you can't see why by looking at the seals and piston, or brine valve.
So does it work right now?