Wiktionary
cut no ice
vb. (context idiomatic usually with "with" English) To have no influence (on).
Usage examples of "cut no ice".
But, strangely, I have a premonition that your explanation is going to cut no ice with me whatsoever, and I will have your badge in my drawer by the end of this shift.
But that would cut no ice with McClennan and Rotterjack, who clearly wanted Hicks away from the center.
However, the words in Diseases of the Sheep cut no ice with magic doorways.
The fact that he'd embarrassed himself even worse cut no ice with her, and understanding why she'd set her flinty little heart on making his life a living hell was no help at all.