The appointments can be marked complete manually from the website in the 'Update Past Jobs' page under the Appointments menu.. You can use this functionality in case the service was not marked complete from the mobile app or you are not using the mobile app to track the services.

The table will list all the appointments whose start time has elapsed and are still in assigned state. You can then select the check box against each appointment and click on Update to Completed or Update to Cancelled to appropriately update the status for the appointments.