You need the Verizon router as the primary router to enable your FiOS TV. Your router can be connected behind the Verizon router, which would double NAT your devices and slow down the connection.
at the link above you can look up how to use only your own router with a MOCA adapter and a few splitters to keep tv without the verizon router.
it is as written a little more difficult to set up but it can be done via your own personal router and then return verizons router to save hundreds a year in rental fees.
but get a receipt showing the return with serial number, your account number, name etc. this way you won’t have to worry about verizon saying you never returned it.
best of luck
In short, it's a pain to use a non-Verizon router with Verizon set-top-boxes. Even more so with the latest boxes, as they require a Verizon router as primary to activate.
Here's the specific FAQ on DSLreports.com that addresses your question: