My Alaska Permanent Fund Dividend payment of $1702 included $298 as an energy relief payment. How do I enter this in TurboTax to back out the tax exempt $298?

You've got the right idea.  First, if you haven't yet entered your Permanent Fund Dividend, please see the TurboTax Help article Where do I enter my Alaska Permanent Fund Dividend? for guidance.

Once that's entered, you need to make an adjustment for the energy relief payment.  To do this in TurboTax Online: 

1. Open TurboTax Online
2. Select  Tax Home in the left pane
3. Select the dropdown to the right of Wages & Income
4. Select  Start or Review/Edit
5. Scroll down and select the dropdown to the right of Less Common Income
6. Select  Edit, Edit/Add or Revisit to the right of Miscellaneous Income, 1099-A, 1099-C
7. On the  Let's Work on Any Miscellaneous Income page, select Start or Revisit to the right of Other reportable income
8. On the  Any Other Taxable Income? page, select Yes
9. On the  Other Taxable Income page, enter Energy Relief Payment in the Description box, and enter your adjustment amount as a negative number (i.e., -662, for example), then select Continue

If the TurboTax Online navigation described above doesn't look like what you're seeing, see the TurboTax Help article Why does the TurboTax navigation menu look different for me?.

From what I have found, the energy rebate is taxable this year.  I know in years past the IRS has posted a notice that it isn't taxable, but all I can find is the FAQ (link below) that was updated in August of 2024 stating that both the dividend and energy rebate portion are taxable.  In years past I believe the IRS has posted their determination part-way through the filing season, so maybe they will again this year.

1099-DIV dividend income 2 | Internal Revenue Service