The "Two" logo may not actually be a Two. You see, what we know is holding up two fingers (index and middle) can also be seen as actually the V for Victory. Seeing that they were "back" after having their case overturned and their ability to practice paranormal investigations again in the city, they updated their logo to actually be a V, because they've got a victory (and is also doubles as a subversion because when you turn your hand around and flash the V, it's actually the British equivalent of the middle finger).
Churchill flashing the V for Victory.
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The Ghostbusters 2 logo:
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As we see with the game, they end up going back to the original logo after some time. So, clearly they did it as a bit of a jab to the local government for trying to keep them from doing what they do best: busting ghosts.