Yes, you can get your money back. You will need to file amended state tax returns for 2018, 2019, and 2020 if you have already filed, @Critter-3 is correct.
Yes, you can do this using TurboTax. It is important to complete Minnesota first. Always end with the state of residence as of December 31.
First, for 2021, file Form MWR, Reciprocity Exemption/Affidavit of Residency for Tax Year 2020 which will stop Minnesota withholding and start North Dakota withholding. Update this form annually.
Second, to fix the prior years:
How do I amend a prior-year state return?
How do I file a nonresident state return?
@dougrox
