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They have 30 days though it is not unusual for them to extend if they receive info from the furnisher that they need additional time to investigate. Are you tracking this online?
If it is a reported collection that was the subject of your prior dispute, then a letter from the creditor would not be relevant to the reporting of the debt collector.
Additionally, the CRAs have a uniform policy that a collection is not to be deleted based on payment of the debt.
What is the stated basis for asserting that the collection should be deleted? If it was that the debt was paid, then the CRA can contest that basis for deletion.
There is no apparent statutory basis requiring deletion of the collection.
Complaints to the CFPB are for review of non-compliance with a provision of statute or regulation.
I do not see a basis for CFPB intervention.
There is no statutory period within which the CFPB must complete an investigation.
Lack of clarity as to the statutory basis for a complaint could result in confusion, and thus delay, in response.