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The more appropriate course would probably be to send a complaint to the CFPB if they faliled to contact you by sending formal dunning notice within 5 days for reporting their collection to the CRA. That is an actual violation of the FDCPA, for which the CFPB has oversightt.
Their failure to have contacted you prior to reporting is not a violation. The basis for any complaint would be their failure to have sent timely dunning notice.
Thus, a complaint wont compel deletion of their proper reporting.
Coplaints to a BBB, who has no legal oversight authority, are used primarily when their action is not per se a violation, but rather a poor business practice.
You can elect to do both, but a CFPB complaint would be my first approach.
However, both approaches dont address the basic issue of their assertion of a debt. They may be found to have been in violation of their dunning notice requirement, but that is a separate debt collection practices violation that might result in a slap of the hand. It does not resolve the primary issue.
If the debt is legit, an alternative is to offer to pay in exchange for their deletion of the collection from your credit report.
If you send a DV, it will place a cease collection bar on them, which does not put them under any period to provide verification.
It requires them to cease collection until they do so, which would include negotitation on ony offer you make.