A "refund" is done on the partial or full amount of an previous "purchase" or "capture" card transaction. A refund is a separate transaction from the original one, and can take up to 10 business days to appear on the cardholder statement (timing is up to card issuer).
IMPORTANT: Should this be a void instead?
If the original transaction was processed today and has yet to be settled, you should perform a "void" instead of a refund. A void will avoid any transaction fees and the original transaction will not appear on the cardholder statement.