Refunds go back automatically on any payment method, and what the closure report tells you.
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When a closure cancels bookings that residents have already paid for, the money goes back to them automatically, on whatever method they paid with. That includes bookings paid outside the card system, for example by transfer or cheque.
For every booking it touched, the report states how much money went back and whether the booking was really cancelled.
The report says so specifically rather than reporting that nothing happened. A booking that was cancelled and refunded is counted, and its refund is included in the total, even when the run could not finish.
Where the system genuinely cannot tell what happened to a resident's money, it says the outcome is unknown and asks you to check that refund against the property's accounts. It will not report zero to mean “nothing moved” when it does not know.
The preview you approve before closing an amenity will tell you if it could not read the bookings, rather than showing “nobody affected”.