Green’s Dictionary of Slang

(US) cheek, insolence.

1930		T. Fredenburgh Soldiers March! 133: I tell them here and now that from this moment on, they will do as they are told when they are told, and I’ll have no backlip or muttering.
1954		Hal Ellson ‘Pistol’ in Tell Them Nothing (1956) 105: She tried to keep me in for giving her back-lip.
1957		(con. 1943) A. Myrer Big War 162: What got into you made you talk like that to the man? Give him that back lip?
1975		E. Torres Carlito’s Way 15: Big Jeff look around like he ain’t even listening, but if you gave backlip — wap!