You have a couple choices. You can not enter the 1099 since the income is tax exempt. The IRS may contact you to follow up on why you didn't report the 1099, and if they do you can respond to their notice by documenting that you received the 1099 because you are a foster care provider.
Another choice is to report the 1099 income, allowing IRS to do their matching process, and then reversing out the income so that your adjusted gross income (AGI) is unchanged.
How enter the 1099:
1. Sign on to TurboTax and continue with your tax return.
2. Click the Federal and Wages & Income tabs
3. Click Start next to "Miscellaneous Income, 1099-A, 1099-C"
4. Click Start next to "Other reportable income"
5. Click Yes when it asks "Any Other Taxable Income?"
6. Enter a description and amount on the page "Other Taxable Income" (ie. 1099 issued by foster care agency). Ignore the warning that says "Do not enter income reported on form 1099-misc.
7. Go back and start the "Miscellaneous Income, 1099A, 1099-C" interview again and follow steps 4 and 5 above.
8. Enter a description and a negative amount. (ie. 1099-Misc. IRC Section 131(a) exclusion of qualified foster care payments.
The steps above will allow you to report the 1099, exclude it from your AGI, and give a reason why
26 U.S. Code § 131 - Certain foster care payments:
