For the Nanny and Household Employee Tax, care.com already paid the amount due for me from schedule H. How do I inform TurboTax that this has already been paid?

[AmeliesUncle]

It sounds like you need to enter that "Estimated Tax" payments were made.  You should be able to enter that into the search box and it should bring you to that section.

[JoannaB2]

No, you don't inform Turbo Tax about your income.  You need to file it on your 2020 income tax return.  Household employee is issued either form W2 or 1099-NEC,. 

A household employee is an individual who is paid to provide a service within their employer's residence. Employers choose what kinds of work a household employee is responsible for and the manner in which that work is expected to be completed.

[Critter-3]

If wages were paid and the payroll taxes where already paid by filing the quarterly payroll reports and a W-2 was issued in January then you do NOT also file the Sch H on your personal return.