Green’s Dictionary of Slang

not care whether school keeps / is kept or not phr.

(US) to care in no way whatsoever.

C. Fowler letter 27 Nov. in Tomlinson Rocky Mountain Sailor (1998) 167: The actual heat in this country does not seem to bother one so much as does the oppressiveness of the climate. It seems to take all the sap out of a fellow and leaves him so that he doesn't care whether school keeps or not.
[US]A.N. Depew Gunner Depew 217: I divided a cigarette with another fellow. Remember, we were sitting and standing on ammunition all this time. It shows how much we cared whether school kept or not.