Currently, the Stay Data API does not include the check-in and check-out time of a reservation within the reservation payload.
The workaround to retrieve the check-in and check-out time for a booking is to configure the booking_changed webhook.
Whenever there is a status change to a reservation (in this case CHECKED_IN and CHECKED_OUT) the booking_changed webhook is automatically triggered. As the webhook should be triggered at the latest a few minutes after the status has been updated (click here to check how often Impala retrieves booking data) recording the timestamp for the triggered webhook will provide the recipient with the CHECKED_IN and CHECKED_OUT time.