According to Ron Lieber for The New York Times, it is possible to cancel a transaction on a debit card by contacting the card issuer. The debit card company often takes the customer's word over the merchant's and either offers a credit or issues a full refund.
The 1975 Fair Credit Billing Act created a process for disputing billing errors, unwanted charges and services and goods that were never received, notes Lieber. Every time a customer disputes a charge, the card issuer has to investigate. The merchant involved in the transaction is contacted and has to provide the card company with proper documentation or a valid receipt of the transaction.