I assume that the taxable amount in box 2a is zero and that box 2b Taxable amount not determined is not marked.
Ask them how they are reconciling their position with instructions for Form 1099-R where for code G they say, "Note. Do not use Code G for a direct rollover from a designated Roth account to a Roth IRA. Use Code H." They'll either have to say that they should be using code H, that the distribution was not from a designated Roth account (despite your assertion that it was) or that they refuse to follow the IRS instructions.
On your tax return, the main thing is that the reporting on Form 1040 lines 5a and 5b are correct, which will be the same for either code G or code H. However, there is no way to enter this Form 1099-R with code G in a way that will cause TurboTax to correctly record your basis in Roth IRA contributions on its IRA Information Worksheet. You can get the desired result on both the tax return and on the IRA Information Worksheet by just changing the code from G to H. There is a slight risk that without submitting a substitute Form 1099-R with code H in box 7 instead of code G the IRS could detect a problem if they do an extensive audit, but that seems unlikely.
