Nope- the letter will be just fine.
There are two ways you can correct erroneous info on a credit report; you can dispute directly with the CRAs (transunion, experian, equifax) or you can ask the credit grantor to correct the issue.
You picked the most direct method. All 3 bureaus should be corrected within the month, and actually if you disputed with one particular reporting agency, they should send you a corrected report for free.
Don't give it a second thought