If Apple replaced the phone under an AppleCare+ with Theft and Loss Coverage plan, they own the old phone. You should contact them to make arrangements to return it to them.
I believe that another circumstance under which you may see a message like this is if you have reported your phone as lost or stolen to your carrier, and they have blacklisted it. In the case where you were not covered by Apple or by anyone else for a replacement, and the phone was blacklisted, you would need to contact the carrier (and prove, to their satisfaction, that you were the owner) if you wanted the phone removed from the blacklist.