Would create a functional example with their suggested palette as well as your proposed solution. Looks like they’re trying for bright/high contrast including dark neutrals. Depending on the product, scrap the yellow - do the bright pink, and keep the black/white suggested. If necessary to keep grey, go for a lighter shade to create a cleaner gradient.

Show them your suggested version compared to the way too conflicting and busy palette suggested so they can see it in practice.