1 (informal) Pilfer or steal (something, especially an item of small value) in a casual way.
Now in that night Boxtel would climb over the wall and, as he knew the position of the bulb which was to produce the grand black tulip, he would filch it; and instead of flowering for Cornelius, it would flower for him, Isaac; he also, instead of Van Baerle, would have the prize of a hundred thousand guilders, not to speak of the sublime honour of calling the new flower Tulipa nigra Boxtellensis, -- a result which would satisfy not only his vengeance, but also his cupidity and his ambition.(Alexandere Dumas, The Black Tulip)
It is base to filch a purse - daring to embezzle a million - but it is immeasurably great to steal a diadem. (Friedrich Schiller, Fiesco or, The Genoese Conspiracy)
'steal,' especially in a small, sly way, 1560s, slang, perhaps from c. 1300 filchenfilzen 'comb through.' (Online Etymological Dictionary)
I am glad I am so acquit of this tinder-box: his thefts were too open; his filching was like an unskilful singer-he kept not time. So says Falstaff in Shakespeare's play The Merry Wives of Windsor. The Bard was fond of filch in both its literal and figurative uses; Iago says to Othello, 'he that filches from me my good name / Robs me of that which not enriches him / And makes me poor indeed.' Filch derives from the Middle English word filchen ('to attack' or 'to steal') and perhaps from Old English gefylce ('band of men, troop, army'). As a noun, filch once referred to a hooked staff used by thieves to snatch articles out of windows and from similar places, but this use is now obsolete. (Merriam-Webster)