Sorry for the confusion. It can be complicated. They are definitely allowed to take the day care credit, regardless of which way you report the income. The only confusion is over how you report the income.
Because you are the taxpayer's parent, they are not subject to the "Nanny tax". Since you baby sat in their home, you may be able to avoid paying social security tax.
In TurboTax, enter at:
Federal Taxes
Click on Wages and Income
Scroll down to Less Common Income
On Miscellaneous Income, 1099-A, 1099-C click the start button
On the next screen click the start button on Other Income not already reported on Form W-2 or Form 1099
Answer Yes on the next screen and enter the amount under Household Employee Wages. Enter the full amount they are claiming even though the screen says enter only if less than $1900 (being the taxpayer's parent waives the $1900 limit).
TurboTax will put the income on line 7 (line 1 tax years 2018 and later) of form 1040 with the notation "HSH". This income is earned income and would qualify for the Earned Income Credit (if you're under 65) and for making an IRA contribution.
You MIGHT not be required to report this as income at all, because it is only a transfer of money between family members, and could be considered a gift, under the right circumstances. But, in order for them to claim the day care credit, you must report it as income.
There is an exception to a grandparent being exempt form the nanny tax: you (the child's parent) "should count wages to your parent if both of the following apply: (a) your child lives with you and is either under age 18 or has a physical or mental condition that requires the personal care of an adult for at least four continuous weeks in a calendar quarter, and (b) you are divorced and have not remarried, or you are a widow or widower, or you are married to and living with a person whose physical or mental condition prevents him or her from caring for your child for at least 4 continuous weeks in a calendar quarter."
