The client always has the right to assert a Reg E claim of transactions being unauthorized. Based on your description of the terms and conditions of the site, it appears you have already opened a Reg E investigation. The customer's failure to review the terms they were agreeing to is not the bank's problem. The transactions are authorized. Send the customer the customer a denial letter and include the terms and conditions as documentation for how you based your decision to deny their Reg E claim.
If, in your opinion, the customer has sufficient cause to pursue a merchant dispute, remember that VISA/MC requires they first attempt to resolve the dispute with the merchant and must include a desciption of these efforts in a dispute letter.
Remember there's a difference between "not benefiting from a transaction because the merchant didn't provide service" and "not benefitting from a transaction because the customer failed to use the service."
V/MC would cover the first statement, but not the second as this is simply buyer's remorse. You could try either "Services not rendered" or "Not as Described" for your chargeback reason depending on what the customer's letter says.
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