Illinois Income Tax Rebate and Property Tax Rebate (Public Act 102-0700) Do these have to be listed for 2022 taxes?

I don’t think that you answered the question.  Illinois issued rebates in September 2022 as rebates to taxpayers who paid Illinois income tax in 2021 and/or property taxes for 2021.  A taxpayer would not have known about these rebates when filing the 2021 fed return.  The question is asking whether to include these rebates in 2022 fed income.  Since the state called these payments rebates not refunds the feds could claim that they should be income if the taxpayer deducted those taxes on his 2021 federal return and should be income even if they did not.  The state has not expressed any opinion on this – it says to ask the IRS.  As you know that is impossible.  The amount of the income tax rebate has nothing to do with the amount of income taxes you paid to the state (and deducted on the federal return) and the property tax rebate is loosely based on the property tax you paid (and deducted).

The taxpayer cannot record this in the state tax refund screen because the related Turbo-Tax questions assume that it is a refund of prior year state income taxes.  But if you include anywhere else in Turbo-Tax then where would you remove it so as not to pay taxes on those rebates?  And maybe the taxpayer should pay taxes on those rebates.

I have no answer.  But that is the issue here.

The IRS has clarified that it will not challenge the treatment of Illinois' property tax rebate as excludable for federal income tax purposes in 2022.  See https://www.irs.gov/newsroom/irs-issues-guidance-on-state-tax-payments-to-help-taxpayers#footnote2