The only thing I can think of is to rub the rehydrated pieces with your fingers to try to free the grit up, then rinse (and strain the rinse water through a wetted towel).
Sorry to be obtuse, but why strain the rinse water through a towel?
Is it so you could use it in the recipe? If so, would a coffee filter work just as well? (I suffer from a surplus of filters and a scarcity of towels.)
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