"Unfortunately, they added the duplicate tax withholding payment to the gross and taxable distribution on my 1099-R and won't correct it to reflect the correct taxable distribution."
This was improper for them to do. They should have added the excess withholding only to boxes 4 and 14, not to box 1. They effectively sent to you or credited to you as tax withholding money that did not actually come from the inherited IRA. Overdrawing an IRA really isn't technically possible, the money had to come from somewhere else and showing it as an overdraft of the IRA is an internal hack. Given that they are refusing to correct the Form 1099-R, you'll need to file a substitute Form 1099-R to correct the gross amount shown in boxes 1 and 2a.
The entire gross amount of the duplicate distribution, including the amount withheld for taxes, does need to be paid back to them. You'll get the excess tax withholding back as part of your tax refund.
