I assume that we are talking about 2025 RMDs since the deadline to take any 2024 RMDs has passed.
As you were informed, you technically impermissibly rolled over an RMD to the IRA and the correction should be to obtain a return of the excess contribution made to the IRA. The total of the RMDs for the 403(b) accounts was required to be satisfied before rolling over anything from either 403(b). (Present IRS guidance for rolling over or converting IRAs says that the total of the RMDs for all the individual's traditional IRAs must be completed before doing any rollovers or Roth conversions from the traditional IRAs, so I assume that the same applies to 403(b) accounts since aggregation is similarly permitted for 403(b) accounts.)
That said, if you just take the combined 403(b) RMD from the remaining 403(b), without a audit the IRS would not be aware that the total of the 403(b) RMDs was not satisfied before doing the rollover. It's your choice whether to roll the dice and hope that the timing issue is never discovered by the IRS. (If it is discovered, you'll likely be subject to accumulated excess-contribution penalties.)
With regard to obtaining the return of excess contribution (the total of the 403(b) RMDs) from the IRA, as long as that is done before the due date of the tax return for the year in which the deposit to the IRA was made (2025 tax year, I assume), there is no penalty that needs to be waived and no requirement to file Form 5329. The rollover from the 403(b) resulted in the distribution of the RMDs for that 403(b) accounts, so there was no failure to take those RMDs. Those RMDs were simply impermissibly rolled over. Your tax return will need to include an explanation statement regarding the return of contribution. What will likely preclude e-filing is the need to split into two the code G 2025 Form 1099-R that will be reporting the rollover, one with code G for the portion permissibly rolled over and one with code 7 for the portion impermissibly rolled over. You'll then be able to prepare outside of TurboTax the explanation statement for the return of contribution and include that with your mailed tax return.
