grime (n.)

1580s, of uncertain origin, probably alteration of Middle English grim "dirt, filth" (early 14c.), from Middle Low German greme "dirt" or another Low German source, from Proto-Germanic *grim- "to smear" (source also of Flemish grijm, Middle Dutch grime "soot, mask"), from PIE root *ghrei- "to rub." The verb was Middle English grymen (mid-15c.) but largely was replaced early 16c. by begrime.

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Definitions of grime from WordNet

grime (v.)
make soiled, filthy, or dirty;
Synonyms: dirty / soil / begrime / colly / bemire