No, I just pump it back into the storage tank. There's a filter on my pump.
Yes I notice particle on the bottom of the jug sometimes. But the line of my pump dosn't reach that low anyway.
I just pour it into a cup and let it settle.

On some models i can connect the intake and muffuler line . On other models it's not that easy.

I also replace or slice the line every so often becuase the tubbing expend and don't fit tightly around the barb from
taking it off and on.