If Airbnb allowed a double booking covering some of the same period as you indicate above, just give them a call @Hannah663 they will be able to check their system and arrange a guest cancellation with no penalty to you.
One thing you mentioned an integration issue. Do you mean you are accepting bookings across different platform and there was a problem with the syncing of your calendars. If this is the case I wouldn't imagine they would consider this , but why not give them a call and see.