Green’s Dictionary of Slang

damp v.2

(US Und.) to steal, by secreting a small object, such as a diamond, in the mouth.

[US]A.H. Lewis ‘The Rat’ in Sandburrs 109: D’ Rat, who all this time is starring his bum lamps, an’ tellin’ how bad an’ weak dey be, an’ how he can hardly see, gets his map down clost to d’ lay-out of sparks [...] It’s now de’ touch comes in. When d’ Rat’s got his smeller right among d’ diamonds, he sticks out his tongue, quick like a toad for a honey-bee, an’ nails a gem. That’s what dey calls ‘dampin’ a diamond.