Green’s Dictionary of Slang

(US Und.) to steal clothes from a clothes-line.

1914		Wash. Post 11 Nov. Miscellany 3/6: ‘Gooseberrying’ is the gentle name for taking clothes from someone else’s clothes line.
1936		Mencken Amer. Lang. (4th edn) 582: To steal washing off the line is to gooseberry it.