[m12k]

This policy is called "fee and dividend", and has a pretty well-fleshed out wikipedia article[1]. IMO it's the best way to implement a carbon tax while avoiding "yellow vest protests" or deepening inequality. A carbon tax will tend to increase the cost of consumption, and consumption makes up a larger part of your income the poorer you are. But with a dividend to give money back to households, you offset this, so a poor household that lowers their carbon footprint enough can even end up ahead.

[1] https://en.wikipedia.org/wiki/Carbon_fee_and_dividend