In "The Quick One" by G. K. Chesterton, Father Brown was talking to his friend, saying:
Didn’t you see how that old man, with the heart of a lion, stood up and forgave his enemy as only fighters can forgive? He jolly well did do what that temperance lecturer talked about; he set an example to us Christians and was a model of Christianity. And when there is foul and secret murder of a man like that — then I do think it matters, matters so much that even the modern machinery of police will be a thing that any respectable person may make use of ... Oh, don’t mention it. And so, for once in a way, I really do want to make use of you.’
I found, in almost every dictionary, that "don't mention it" is "A polite expression used to indicate that an apology or an expression of thanks is not necessary."
But that doesn't make sense in this context, so I guess that he mean "shut up my mouth" because he praised himself as a respectable man, doesn't he?