"ancient tool for scraping the skin after a bath," 1580s, from Latin strigilis "scraper, horse-comb," from stringere (1) "draw along a surface, graze, touch lightly; strip off, pluck off, cut away; clip, prune; lay bare, unsheathe," figuratively "waste, consume, reduce; touch, move, affect, cause pain," from PIE root *strig- "to stroke, rub, press" (source also of Latin striga "stroke, strike, furrow," stria "furrow, channel;" Old Church Slavonic striga "shear;" Old English stracian "to stroke;" German streichen "to stroke, rub").
Etymologists dispute over whether this is connected to Latin stringere (2) "to tie, tighten," root of strain (v.). Based on the sense differences, de Vaan writes, "It appears that a merger occurred of two different PIE verbs, *strig- 'to brush, strip' and *strengh- 'to tie'."