I think that the letter that you are drafting is the appropriate response.
Check the Form 1099-R in your Wage and Income Transcript to see if the $597 is present for box 4 Tax Withholding. The Record of Account combines only your Account Transcript and your Tax Return Transcript, so not all of the necessary information is there. The Tax Return Transcript will only show what you reported on your on your original tax return, it does not get updated to show the results of any amendment. (I don't know how the tax withholding might appear in your Account Transcript. Being self-employed, the only tax payments I make are estimated tax payments, so I have no tax-withholding record for comparison.)
Amendments are processed by people at the IRS and people make mistakes. It seems that you correctly prepared the amendment [assuming that you attached the Form 1099-R to the amendment as Critter indicated above] but the individual processing the amendment failed to recognize that the originally omitted Form 1099-R had tax withholding that needed to be considered or the payment made with the amendment got processed but the amendment itself has not yet been processed. Check the status of your amendment here:
https://www.irs.gov/filing/wheres-my-amended-return
($597 is a bit of an unusual amount of withholding on a $2,600 taxable distribution. The mandatory minimum withholding is 20% and would have been $520. If you requested withholding above that specified as a percentage, an additional 3% would have been $78 for a total of $598.)
