So the rules states that a formation is driven back when one or more companies is removed by a single shooting attack. So does this mean an entire eight man infantry company or when a company movement tray is removed?

For example, you have three companies of orcs, two are full with eight models, and one company has one model left. In a shooting attack, a hit is scored and the movement tray is removed. Does the formation fall back for just losing the one model?

In your example - yes.

Obviously, there is an abstraction taking place. You choose to shoot at a formation (with all fresh companies), do 7 casualties and fail to drive them back. (The fellas must have been determined to hold their ground) Later, you shoot at the same formation, this time killing only one (but finishing off that company with only one guy left) and drive them back. (The poor fellas are starting to think twice about the ground they hold)

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Incoming fire has the right of way...