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Did you send them a written notice?
Do you have available copies of all letters/emails?
Since you have a copy of the cleared check, your next step is the CFPB: https://help.consumerfinance.gov/app/creditcard/ask
(Just don't expect a response from either Barclay's or the CFPB tomorrow... Federal holiday.)
The next step is to file a formal dispute under the FCBA for violation of the posting requirement of that statute.
The FCBA dispute process has teeth. Check out the summary on the FTC web page.
I would first complete the FCBA dispute process and obtain resollution prior to pursing the credit reporting issue under the FCRA, for which you can file a complaint with the CFPB. Resolution of the FCBA dispute should take care of the FCRA reporting issue.
iv:
Yes, I have provided Barclays with written notice, and I have retained all copies of the documentation. I will file a complaint with the CFPB. Thank you for the guidance.
RobertEG:
Thank you for the response. I have just submitted a formal dispute through the FTC website.
Can you see your account number referenced on the check copy? I can see them responding that they couldn't link it to your account.
GL