Transfer Ownership: Record View Permission

If an internal user/owner transfer ownership of a record to an external user, this new owner will have all privileges of a BP owner, and the originator name on the BP form and the log will show the new owner.

If we transfer ownership back from the external user to the internal user/owner, should it also revoke the privileges that the external user had? We tested this on our stage environment and this did not happen. External user is still able to view the record with the new internal owner.