I wouldn't take the box out. If it belongs to Verizon, it's either critical copper or Fiber infrastructure. This may be sitting on an easement where Verizon has the right of way. Those green boxes can also contain high voltage electrical wiring, or Cable TV infrastructure.
If the box is in the ground, and is supposed to be flat, use some dirt to fill in the cracks around the box, but do not cover the box up. If it's a pedestal, it should be left alone. You are free to use dirt to fill in the area under the pedestal if the copper/fiber plant has lifted up the pedestal from the ground.
