What will you answer to the compliments out of politeness?
It is under this situation, if someone flattered you after you said sorry about your messy appearance due to run out of time to fix about your appearance.
(I am appreciate it if you tell me any other way to show your gratitude.)
1) Thank you for your politeness.
2) Thank you for the careful remarks.
3) Thank you for saying that.

Question

Answer

Hi Maya

1) Thank you for your politeness. - This is extremely formal. So not something that people would normally say. 
2) Thank you for the careful remarks. - 'careful' is not really the appropriate word in this context.
3) Thank you for saying that. - This is the best of the three. Sounds very normal.

You could also say "Thank you for your kind words." - which is also quite formal. If it is a friend then you might say "Thanks. You are kind." You would normally stress the word 'are' to show how genuine your statement is.

Hope this helps

Chris