they gasped at the impertinence of the suggestion
impudence: an impudent statement
crust: the trait of being rude and impertinent; inclined to take liberties
(impertinent) characterized by a lightly pert and exuberant quality; "a certain irreverent gaiety and ease of manner"
(impertinent) extraneous: not pertinent to the matter under consideration; "an issue extraneous to the debate"; "the price was immaterial"; "mentioned several impertinent facts before finally coming to the point"
(impertinent) fresh: improperly forward or bold; "don't be fresh with me"; "impertinent of a child to lecture a grownup"; "an impudent boy given to insulting strangers"; "Don't get wise with me!"
Lack of pertinence; irrelevance; An instance of this; a moment of being impertinent; The fact or character of being out of place; inappropriateness; insolence
(impertinent) insolent, ill-mannered; irrelevant (opposite of pertinent)
Irrelevancy; the flaw of bearing no reasonable relationship to the issues or proceeding at hand.