The original suggestion could be collected at point-of-sale for carbon emitting products. Gasoline, airplane tickets (based on average for the flights), even electricity are easy to measure and charge at the point of sale.
In your example, the person has to prove how much they didn’t emit, which is way harder in practice, to get the credit.
And similarly i would extrapolate to do we tax the buyer of electricity (which could be green sourced) or the manufacturer - the gas burner. Or maybe even at the first point of contact with the carbon source, the oil company.
So you're saying that the government should incentivize poorer people to sell one of the last bits of their functional autonomy for what would be trivial amounts? "We'll just hang onto to this for a bit until you decide to stop going anywhere or make friends at work".