Green’s Dictionary of Slang

1. to ignore, to overlook.

1842		Cambridge Chron. 29 Oct. 2/2: Party-wreiters sometimes make small bones of consistency.
1846		Era (London) 9 Aug. 7/1: Money has been called the sinews of war, but ministers make small bones of it.
1888		Sun (NY) 13 May 9/1: If he has a tough job [...] he will do it with an [...] imperturbable good nature that goes far to make small bones of the complainants’ troubles.
1935		Brooklyn Dly Eagle (NY) 19 Mar. 20/6: The author [...] makes small bones of the fact that the young man had not behaved any better than he should.
1940		Brooklyn Dly Eagle (NY) 26 May 42/2: Sentiment in U.S.A. makes small bones of the fact that the high command is right.

2. to deal with easily.

1849		Freeman’s Jrnl (Dublin) 17 Feb. 3/1: The Austrians woiuld make small bones of blowing Venice into the sea, if they could do so.
1858		Dly News 5 Feb. 6/2: The Porte makes small bones of displacing a Pacha who has made himself obnoxious.
1873		Times-Picayune (New Orleans, LA) 15 Aug. 8/5: When Jim Jime gets started he makes small bones of anybody.
1885		Bulletin (Sydney) 31 Jan. 13/1: Pearce made small bones of a 60lb impost, and won the all-comers’ light skiff handicap.
1901		Chicago Trib. 20 Feb. 6/5: Having long defied the state of nature, Dr Dowrie makes small bones of defying the state of illinois.