To steal or purloin. A filch is a staff with a hook at the end, for plucking clothes from hedges and abstracting articles from shop windows. Probably it is a corruption of pilfer. (Welsh, yspeilio and yspeiliwr; Spanish, pellizcar: French, piller and peler. Filch and pilfer are variants of the same word.
“With cunning hast thou filched my daughter's heart.”
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
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