I suspect they are intended to reduce radiation of interference from the circuitry inside, though they may also be used as a heatsink if there any components attached to the inside of the metal.
The metal shield, if left off, might cause noise for radio, TV and cell phones.
The monitor will work. The case might not go back on. The stand bolts into some of the metal.
If it has no components mounted on it, the monitor should work just fine. There will be more interference from the monitor than there would be with the cover but if there is nothing susceptible nearby then there is no problem.