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FCRA 623(a)(4) specifically requires a creditor who has reported an account to a CRA to provide notice to the CRA in their next regular reporting cycle of anyrequest for closure of an account by the consumer.
If the account is showing in your credit report, they are subject to section 623(a)(4), and it is thus a violation of the FCRA for them to decline to report closure of the account by the consumer to the CRA.
If they cannot locate your account, they could then delete all reporting, but cannot have it both ways.
I would send them formal written notice of your request to close the account.
If they then formally decline to make the required update, you have a documented and willful violation on their part of the FCRA, subjecting them to civil damages under FCRA 616 which can include punitive damages and costs of the action, including court and attorney fees.