Void, same day: in Payment History, a Manifold Pay charge shows "Void on Terminal". Voiding cancels the charge at the terminal so it never settles. It only works before the terminal batch settles (Batch Out / end of day). After settlement, refund instead.
Refund to the card: card refunds go through the normal Issue Refund flow. Allocate the refund to "Manifold Pay" and issue it; the refund runs on the terminal, and the customer must tap or insert their card to receive the money. The terminal refund completes first and only then is the refund recorded in Manifold, so if the card is never presented, nothing is recorded and the invoice is unchanged.
If the invoice also holds money taken on another processor, the modal shows an External Card row beside Manifold Pay, each capped at what was paid that way. An External Card refund is only recorded in Manifold; run the refund on your other processor yourself, the same way you took the payment.
Refunds by cash, check, or store credit on the same invoice work exactly as they do without a terminal.