cut ice
cut ice {v. phr.}, {informal}
To make a difference; make an impression; be accepted as important. — Usually used in negative, interrogative, or conditional sentences.
When Frank had found a movie he liked, what others said cut no ice with him.
Jones is democratic; a man's money or importance never cuts any ice with him.
Does comfort cut any ice with you?
I don't know if beauty in a woman cuts any ice with him.
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Source: A Dictionary of American Idioms