What Bill said plus the following:
Inside the dome you're talking about is a tiny dish antenna. The actual dish (reflector only, NOT the microphones) is the ONLY part of the whole equation that could be reused, but because it is tiny it's the one piece you'd never want to use.
If you google "L-com" you'll find dish cell antennas as big as four feet in diameter. Compare that to the 8-inch dish inside the dome you're talking about. Moreover, these antennas are fairly cheap, MUCH less than the cost of the parts to try and use a pre-existing dish reflector.
Once you've got the dish your troubles are only beginning. You have to know EXACTLY where the cell tower is, and these dishes have a beam width of about 6 degrees, which means that if your aim was off slightly you would get zero signal.
There is a DIY project to convert a large open-face TV dish to a wifi antenna. As said, everything needs to be replaced except the reflector (dish), but once you're done you have a wifi antenna whose reception is only limited by the curvature of the earth.
Again, L-com sells 4-foot versions of these that are extraordinarily powerful. Back in the early days I considered using one of these to pull in a Boingo wifi signal from three miles away over water. Nowadays grandfathered cell data is so good there really isn't any need.
