It's taxable income, to them, whether it's reported as household employee (HSH) or self employed income. If reported as self employment, TurboTax (TT) will calculate self employment tax (SET - social security & medicare) in addition to income tax. There is no way to indicate being a caregiver to their grandchildren, to avoid SET.
In TT, you ignore the $2200 HSH limit, as it doesn't apply to grandparents. TT will not block you, from continuing, when you enter a larger amount.
