dregs, grounds
滓 centers on the leftover sediment or residue that settles out of a liquid: dregs or grounds, the unwanted solid bits that remain after brewing or steeping.
滓 combines 氵 (water) with 宰, which likely contributes the sound and the idea of something being processed or left behind, together suggesting the dregs that settle in water.
Water 氵 plus 宰 (which can suggest managing or processing) gives the image of managing water and finding the leftover grounds at the bottom: the dregs.
For シ, picture a sheet of paper filtering out the dregs from tea: sheet -> シ, and the sheet catches all the grounds.