When performing a Restore or Clone operation in Backup My Org for the purposes of migrating items, you will find that restored registered service items are still pointing to its original data source.
This is working as intended. Registered service items in an organization exists only as a pointer to data located elsewhere. When this item is migrated or restored, it still maintains it’s status as a registered service item on the destination pointing to the same data source.
At this time, Backup My Org does has an experimental backup option: “Backup Registered Services as Hosted.” However please note that there are many variables to determine the eligibility for certain registered services to be hosted, including (but not limited to) being shared publicly, sync capability settings, etc.