After you file

See the following from TurboTax:

Q: Where can I go to opt out of receiving marketing e-mails? 
A:
 Customers can manage their contact options by visiting us at Privacy Preferences.

Q: I opted out of marketing contacts from Intuit, why am I still getting e-mails?
A:
 Your choice to opt-out only applies to promotional materials and not critical service notifications that could affect your service or software. Intuit respects your desire to not be contacted. We notify our customers about "critical service notices" because it may be necessary to contact customers to notify them about subscription expirations, provide order information such as confirmations, or alert them to an issue with a service or software that could negatively affect their continued use. Due to the financial nature of our products, customers cannot opt out of receiving these critical service notifications. We take care to limit these notices only to customers affected by the issue. Also, please note that if you have more than one email address, you can opt out of one and not the other(s).

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If you need more help you can contact TurboTax Support

https://support.turbotax.intuit.com/contact/