It's/that's no skin off my nose British informal
In some cases, this idiom is also known as "it's no skin off my back" in US culture.
Used when you want to imply whatever people do doesn't affect or make any difference or harm to you and you don't care about how the result will be
Listen! This mess is your fault, not mine, so stop yelling at me like I am the one who is responsible for that. It's no skin off my nose!
Getting back with her ex? Ah hah, just let her go ahead, it's no skin off my nose. She will not listen to my advice anyway.
It's no skin off my nose when you wear make-up or not, because I love you just the way you are.
This idiom is often used to express that you should accept an unpleasant situation or event because you cannot change it.
Once something has been done, you can do nothing but face the consequences.
This idiom is usually used in present tense.
"No skin off my nose" is believed to have origin from boxing but there's still another more creepy one. In 16th century England, an unsavoury cult existed and the King managed his men onto the streets to disassemble their gatherings. A reaction was given by the cult that they pierce a small hole in the door wherever they met. Worshipers would draw a small mole on their nose as a signal and would have to press their noses through that hole to enter. And if there was no mole, a slice of skin would be taken off with a sharp implement because they believe that person was the King's man.