no skin off one's teeth

From a confusion of no skin off one's back/nose with by the skin of one's teeth.

• "No skin off our teeth, right, boys?"
• "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."
• "So you're not interested in learning? No skin off my teeth."

• no skin off one's back
• no skin off one's nose