"Don't look a gift horse in the mouth" synonyms

Related, but also antiquated: "Don't bite the hand that feeds you!"

“Don't look a gift horse in the mouth” synonyms?

ingratitude or to be ungrateful OED

1. Want or absence of gratitude; indisposition to acknowledge or reciprocate benefits received; unthankfulness; ungratefulness.

As in:

Defeating ingratitude in our kids is largely dependent on them seeing gratitude in us. Fox News Nov 18, 2018

You could consider the more modern:

Don't look at gift's price tag (PowerThesaurus)

In the description of the expression you are giving, Urban dictionary says:

You look in a horse's mouth to determine its age and/or health. So if someone gives you a horse, and you look in it's mouth, it's like looking for a price tag. It's rude!