@Toni222,
The information that @Emiel1 gave you about hosts changing the date is incorrect. First, a check-in date cannot be changed after the booking period has started. Secondly, if the host were to change the date, the reservation will get a new cancellation window based upon the date of the change. Thus allowing the guest an opportunity to cancel, and get a full refund minus the service fee. Instead, in these situations the guest should submit a date change request, and the host can accept or decline it. https://www.airbnb.com/help/article/1504/how-does-it-work-if-a-guest-wants-to-change-their-reservati...
Since the reservation has already started, the dates cannot be changed. I would not offer a refund, but would give the guest the opportunity to book in the future off platform. If you do that, inform the guest that they will have to provide a refundable damages deposit.