TurboTax does not receive any information about your refund after you file your tax return. The way to know that a mailed return was received would be to use a mailing service like certified mail so that you get a confirmation that it was received. You can track it yourself:
To check the status of the rent credit in MN
http://www.revenue.state.mn.us/individuals/individ_income/pages/draft-wmr-context-page.aspx
https://www.revenue.state.mn.us/wheres-my-refund
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