Old Devices on Recently Installed Modem/Router

I recently had Cox internet service started in my home. I paid for installation of their rental modem/router. Service is great, but I recently discovered that devices from the previous user(s) are still saved onto the router. I messaged with a COX rep to voice my concern, but was told he didn't understand what the issue was an recommended I pay $10 more a month for Cox Complete Care. He also told me devices could not be saved onto the device. Huh? Am I wrong to think this is a justifiable security concern? I've already removed those devices from the router, but I feel a full reset should have been prior to installation.