no skin off one's teeth en · X
Etymology
From a confusion of no skin off one's back/nose with by the skin of one's teeth.
Meanings
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(idiomatic, informal) Of no consequence to one.
So you're not interested in learning? No skin off my teeth.
2015, Glenn Beck, Agenda 21: Into the Shadows, page 321:IT IS NO skin off our teeth to grant that other creatures may have their wants, needs, and passions as well as varying degrees of intelligence, geniality, and perhaps compassion.
2014, John Edward Terrell, A Talent for Friendship:No skin off our teeth, right, boys?
2014, George Donnelly, Lando Cruz and the Coup Conspiracy: