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Lied to you about owning the debt, or about what they were authroized to agree to in a settlement?
Whether or not they are truthful on those points is immaterial to their acceptance of a PFD. If you have a successul basis for complaint, it would not relate to the validity of either the debt or of their collection authoriyt per se, and thus would not be the basis for requiring CR deletion.
Settling of less and/or granting CR deletion are optional and discretionary on their part.
When they sent dunning notice, who was identified as the party who owned the debt, and thus who they were collecting on behalf of?
Is the OC reporting, and if so, are they reporting a $0 balance?
Have you had confirmation from the OC that they no longer own the debt?
Then if you feel that they are being deceptive as a tactic to further collection of the debt, you could file a formal complaint with the CFPB.
However, you are seeking their good-will acceptance of your request for deletion, and/or of acceptance of less than the full debt as settlement.
Result may be a slap on their wrist, but I do not anticiapate any order by the CFPB of deletion of their collection as a sanction. That is, in my opinion, an unrelated matter beyond the scope of the CFPB admin process.
Thus, I would not take the path of filing a complaint, as it is not apt to improve their feeling of good will.