There is no requirment under the FCRA for a first debt collector to delete their reported collection once they no longer have collection authority.
However, the CRAs have an administrative policy that a debt collector delete when their collection authority is terminated and the debt remains unpaid.
That policy is specifically stated in their joint credit reporting manual.
Thus, the procedure is to notify the CRA, such as by way of dispute, of the lack of deletion by the first debt collector.
They will then delete based on their own policy.
