I got a letter today saying: "Copy of the other state's tax return was not received for Credit for Tax Paid to Another State." Shouldn't TurboTax have done this for me?

yes, Turbotax should have submitted a copy of the non-resident return if the resident state's tax laws so require. to late now. do what the notice says.   This could be an issue at your resident state level rather than a Turbotax problem. i've seen no other threads concerning the same issue as yours.

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There was an issue with GA a few weeks ago.  When did you file?

I filed on April 17th.

Do you know if there is a way that we could confirm that TurboTax has transmitted the requested non-resident return copy? I'd like to double-check with the state customer services if possible.