If a customer cancels a hotel booking made through the API, how does the refund reach them?

Yes, cancellations can be handled through the same connection that made the booking, but the money comes back on the supplier's terms and not on yours. When your customer asks to cancel, your site sends that request through to the supplier holding the reservation. The supplier checks the rate rules attached to that particular room and decides what, if anything, is refundable. Your booking page then shows the outcome.

The important part to understand is that the rules travel with the rate, not with your website. A room sold as fully flexible will usually cancel cleanly up to a deadline set by the hotel, while a cheaper advance rate may be non refundable from the moment it is confirmed. That is why two bookings made on the same day for the same property can end very differently, and why it is worth showing the cancellation terms clearly to the customer before they pay.

How the refund actually reaches the traveller depends on how the payment was taken. If the customer paid you and you settled with the supplier, the refund lands back with you first and you return it to the customer. If the payment went straight through to the supplier, they will process it back to the original card. Timing is set by the supplier and the banks in between, so it is honest to tell customers it takes a few working days rather than promising it will be instant.

Before you go live, run a test booking and then cancel it, so you can see exactly what your customers will be told and how long the money takes to come back.