You don't have to do anything. Payments will be sent automatically to people who are eligible. Please see the settlement web site for information about settlement payments. Note the following statements from that web site.
"Consumers to Receive Payments Automatically, Without Filing a Claim"
"The settlement is being administered by a third-party administrator, please do not contact Intuit [TurboTax] with questions."
You should also look at the Common Questions on the settlement web site.
The checks are being sent by the settlement administrator, not by TurboTax.
You cannot sign up for the settlement. The settlement applies to a very specific set of circumstances. If you are a "Covered Consumer" as defined in the settlement, you will automatically be sent a notice and a payment. You do not have to do anything to be included, and there is nothing that you can do. Most TurboTax users are not Covered Consumers. Here is the definition of "Covered Consumer" from the settlement agreement.
"Covered Consumer" means any individual, or individuals if a joint return was filed, who in Tax Years 2016, 2017, or 2018 was (1) eligible to use an Intuit IRS Free File Product; (2) began his or her tax returns using a TurboTax Free Edition Product; (3) was informed that he or she was ineligible to use a TurboTax Free Edition Product; (4) subsequently paid to use a TurboTax Paid Product, and (5) had not used the Intuit IRS Free File Product in a previous tax year.
