Not quite sure about the right expression

[cyrildelarama]

hello teacher!
can you please help me.
I'm interested to know the right expression - sounds like "no skin off my teeth"? or something like that.
What does it mean?
appreciate your quick reply.
thanks
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[Casiopea]

Welcome, cyrildelarama.

The idiom by the skin of one’s teeth means, “barely survived”.
EX: I passed the exam by the skin of my teeth.

The idiom no skin off my nose means, it has nothing to do with me so it doesn't matter to me.
EX: It's no skin of my nose that Max didn't show up for the exam.