Here's what I did:
I had this issue pop up after installing 'My Verizon' after I flashed Hyperdrive15 to my GS4. I didn't respond to the request and just let it time out.
I then force-closed My Verizon.
Using Xposed Framework:
I added it to the RootCloak module.
I used the module 'App Settings' (ver 1.8) and removed the following permissions from 'My Verizon Mobile':
I believe these are most likely so the app can act as a security app in case the phone is lost or stolen. VZW offers a 'premium' insurance for US$10 a month that provides the features. They try and push it down your throat every time you ask about insurance or add a phone. I keep telling them there are plenty of free apps that do the same things and more for free.
Anyhow, that's what these perms are most likely for, however, like most things in life they can be used for other things by big red I'm sure. Especially the GET_TASKS perm.