no skin off (one's) teeth

No cause of concern or interest to one; no source of difficulty, threat, or risk. Hey, it's no skin off my teeth if you want to get a tattoo. I'm just saying that it's something you may regret someday. A: "Do you mind if I store some of my stuff in your garage for a while?" B: "Eh, it's no skin off my teeth."

no skin off someone's teeth

and no skin off someone's nose

Fig. no difficulty for someone; no cause for concern to someone. It's no skin off my nose if she wants to act that way. She said it was no skin off her teeth if we wanted to sell the house.