it’s no skin off my, your, his, etc. nose

[Daruma]

Do you say "(It's) No skin off my nose" as an answer for "Thank you"?

it’s no skin off my, your, his, etc. nose (informal) used to say that sb is not upset or annoyed about sth because it does not affect them in a bad way

Merriam-Webster's Learner's Dictionary
no skin off my nose
informal —used to say that you do not care or do not have a strong opinion about something
▪ Go if you like—it's no skin off my nose.

[buggles]

To use that as a response to someone saying thank you to you would be regarded as somewhat impolite.

It conveys to the person thanking you that you don't really care about what they do or think.

If they've thanked you, it shows they appreciate whatever you did to earn their thanks. To reply, "It's no skin off my nose." tells them their appreciation is neither here nor there to you.

Much better to just say, "You're welcome" or "No problem" or "That's OK".

buggles(not a teacher)

[wace]

Fairly good examples could be:

'If she doesn't want to help me, it's no skin off my nose'
'Let them cancel the whole project. It's no skin off my nose'
'It's no skin off my nose if you don't take my advice'

[Philly]

Saying "it's no skin off my nose" instead of "thank you" strikes me as being so completely wrong and inappropriate that it might well cause the other person to laugh.

Non-native speakers of any language often make funny mistakes. I've made mistakes when speaking German that my German friends found side-splittingly hilarious.

[svartnik]

Originally Posted by Philly

Saying "it's no skin off my nose" instead of "thank you" strikes me as being so completely wrong and inappropriate that it might well cause the other person to laugh.

Non-native speakers of any language often make funny mistakes. I've made mistakes when speaking German that my German friends found side-splittingly hilarious.

In this respect, I would make a highly-regarded stand-up comedian in any English-speaking country.

[Raymott]

Originally Posted by Philly

Saying "it's no skin off my nose" instead of "thank you" strikes me as being so completely wrong and inappropriate that it might well cause the other person to laugh.

The question was about this phrase as a reply to 'thank you', not instead of.
In either case, it would generally be inappropriate.

[Philly]

a reply to 'thank you', not instead of.

Oh, sorry, I actually did understand that. Thanks for mentioning it.
I guess my memories of providing unintended humor for my German friends must have gotten me so sidetracked that I ended up losing track of the original question.