A lady, in declining a proposal, is said to give the gentleman the mitten.
1844. Young gentlemen that have got the mitten, or young gentlemen who think they are going to get the mitten, always sythe [sigh].J. C. Neal, Peter Ploddy, &c., 14. (N.E.D.)
1853. Uncle Jos gal gin him the mitten, to the singin school.Turnover: a Tale of New Hampshire, p. 8 (Boston).
1855. Well, I did think Harry was one time tender upon Kitty; but he went off suddenly to California; likely enough, Kitty gave him the mitten.D. G. Mitchell, Fudge Doings, ii. 116.
1856. As if I should believe you had given that nice young man the mitten.Knick. Mag., xlviii. 16 (July).