Tivo Premiere?

Hello jeffboswell

As you are having a SBG10 , to check on the list of connected devices kindly follow the steps below : 

1. Connect to Wi-Fi on any of your devices 

2. Launch a web browser, such as Internet Explorer, Firefox, or Safari.  Enter http://192.168.0.1 into the address box, and press the Enter key. 

3. Login on the web manager page . On the 2.4Ghz and 5 Ghz please check on wireless client list the connected devices if you still see the TiVo Premiere then lets do a  Factory Reset 
4. To do a Factory Reset please follow the below link 
5. http://arris.force.com/consumers/articles/General_FAQs/SBG10-Factory-Reset

After Factory Reset done , check if TiVo Premier is still seen in the list. Also, could you let us know from where and when did you purchase the modem!!

Hope this helps, if you any more queries do let us know . 

Before you factory reset, I suggest looking up the device mac address with MAC address lookup site to confirm the vendor.  Check in the SBG10 client list to confirm if that Tivo device is connected via hardwire or Wi-Fi.  If connected via Wi-Fi, you can filter mac address to block that client from Wi-Fi network.