We are denying a Reg E claim (customer ordered goods but not happy with them). Didn't do much of an investigation because it was pretty cut and dry. Since this isn't an "unauthorized" card transaction" under the definition, do I even have to do an investigation? Also, would I even need to send the customer a letter telling them the claim was denied? I would like to spend less time and just call the customer.

The extent of your investigation is the determination that it does not meet the definition of a valid claim under Reg E.

If it's not a valid claim, then the notification requirements don't come into play, but from a customer service standpoint, I'd at least call the customer to let them know what is going on.

You may have an obligation under MC or VISA rules (assuming the transaction ran as a signature debit) to attempt resolution for your customer.

VISA and MC don't not offer the cardholder protection for "buyer's remorse." However, if the product was in some way defective, wrong color, not as advertised, etc., there may be chargeback rights available. In all of these cases, VISA and MC will require that the cardholder first make an effort to resolve the situation with the merchant. If they are not successful, they should document these efforts in a dispute letter and include a detailed description of what went wrong. Since this dispute is not covered under Reg E as you've already properly denied the Reg E claim, you are not bound by the 90 day investigation time frame.