In short, there is no publicly verified information indicating that Hall and Oates have a restraining order against one another.
Daryl Hall and John Oates are a long standing pop rock duo, and over their decades long partnership they have had public disagreements, business disputes, and periods of estrangement, yet available court records and credible reporting do not confirm any active or historical restraining order.
This status clarifies the legal and personal context, defines what restraining orders entail, and explains how rumors like this spread within the music industry.