I need to reproduce it and show it to the Verizon people ....and at that time I will ask for a replacement.
That is strange, I've never heard of that on TV's or any phone screen either. When your screen wakes up like that, are you able to get it to go away without turning the screen off and back on again, or does it just stay that way?
Just a heads up, go ahead replicate the issue on your own, and seriously just take a pic of your phone in that state with a digicam or another phone to have it documented. The store people or manager won't replace it on your word without straight up seeing an obvious defect. They'll mess with it, turn the phone off/on, reboot it or whatever, and also almost certainly will want to do a factory reset, if you let them... but it's really part of their troubleshooting. Needs to be an obvious defect for an "easy" worry-free on the spot exchange. Definitely snap a pic of it if you can with another camera and bring that with you for sure.
On the other hand, it may be easier to get an exchange period new replacement over the phone, and I would try that first honestly... just say it's definitely doing it, and it's brand-new etc., and have them Fedex you a new one. They'll have to charge you up front though, and may charge full retail, and then credit your card when they scan the defective one back in their warehouse. Did you pick this one up at the store or online/over the phone? Some retail store (or most these days) managers will say on the spot that they won't exchange your device if it wasn't purchased from an area corporate store... Just a heads up, this happened to me more than once, eventually was taken care of over the phone through supervisor CS. So it was hassle-free but I was charged up front of course, there's no way to avoid that for a new replacement.