The carbon tax isn't a traditional tax, the money collected is pooled and paid back out evenly to households.

This means as long as a household is producing less carbon than the average, they get more money back from the rebate then they paid into it.

High income people still currently produce significantly more carbon than poorer households. The last time I looked at the numbers, something like 60% of households got more money back from the program, and nearly all poorer households fall into that.

Yes there are likely outlier poorer households who also produce way more carbon, but when looking at the system overall they are the exception and could likely fix their situation by changing their behaviour.

To reiterate, this is not a tax because the income doesn't go into the governments income, reducing the income tax has no impact on government revenue. The majority of poorer households get more money back from the carbon rebate system.