I am assuming you are speaking of the "Virtual Machine Disk Format", this is a system file that monitors the hidden system partition on a device..
The only thing is I am unsure why you are using data for it, I believe it could be coming from another application that is accessing the files data by unclear whats with the data use.
What plan are you on? This is new to me, and have never seen someone charged for VMDF... What device are you using, and what applications do you have installed? Have to tried calling CS to see if they know anything about it? The only possible way I can see a VMDF is if you use Verizon's backup assistant though I would also assume they would bill it or word it something most people would understand.
Tidbit makes a valid point about Verizon's Backup Assistant and from my experience this is one of the applications that causes data transfer another thing is any application that is intended to sync data to a cloud base service..
Basically what I do is use Onavo Count and set all the apps that access Cloud base services to WiFi only so it can not use the devices data to sync because sometimes apps like this can sync a gig or more data in one day that can get costly if using a tiered data plan.