Pretty sure they're considered expendable -- particularly if they are non-functional. So you could most likely just pitch it.
The last time I swapped a STB, I tossed the three broken remotes I had collecting dust in my drawer back in the box and sent them back to them. I figured if that could make use of them great, and if not, they'd take care of pitching or recycling them.
If Verizon didn't give you any information on how to return it, I would assume they don't want it back. I have to figure that they are paying on the order of $10 each for the remote. I doubt Verizon could handle the paperwork and shipping cost for $10, so it isn't worth it to them to get it back..
I'd just dispose of it.
Or you could drop it off at a local store if one is convenient to your location.
Any old remotes that you may have do not need to be returned. You can go ahead and discard the old remote.
§MC§