Is there a relationship between 'politeness maxims' and 'compliment responses'?

In my response, "politeness maxim" is taken to mean "a very common phrase that people say to each other with the aim of not communicating new knowledge but to be friendly, nice, etc." e.g. When a co-worker tells you that a relative died, it is common for people to say "I'm sorry to hear that" which is a politeness maxim.

"compliment response" is taken to mean "a very common phrase that people say after another person has praised them for ability, possession, appearance, or anything that is valuable for social or economic reasons." E.g. When a person says you look so pretty, people may say "you don't have to say that" or, "no I don't, you're just being nice." These are examples of compliment responses.

Incidentally, I believe that the best response to a compliment is to say "thank you."

Given these two definitions, then yes, there is a relationship between "politeness maxim" and "compliment response." They are both common linguistic formulae rooted in culture with the aim of facilitating social relationships.