Give 'em the business
Language Log has an interesting mention of strange phrasing in a Slate summary of a USA Today story: "USA Today leads with word that one-third of the 1,600 former soldiers who've been ordered back into service are giving the Army the hand and haven't shown up."
Had I read this on my own, I'm not sure I would have understood the meaning. But Mark Liberman's explanation makes sense:
I guess this is a blend of the idiom "give the finger toTo me, it sounds like a euphemism for "giving the Army the finger."
" and the catch phrase of a few years ago "talk to the hand", with its associated gesture. There's a stark contrast between giving someone a hand and giving them the hand: not your standard semantics of definiteness.