I've been trying to work out which paper you mean, the cover at the back of the neck board (Pic 3)?
And TOTALLY agree with LTG, be very bloody careful any time you are playing around at the back of a CRT monitor, especially around the anode cap (rubber cap with lead coming off it). There is a procedure to discharge a monitor, definitely google it first but if your still not sure then ask! I would also wait at least 12-24 hours after you have last powered on the machine before you go to discharge the monitor, it will still have charge mind you, and can still be lethal.

Mine has got one but it may depend on which chassis you have too, think these machines were either Wells Gardner or Ducksan

AHHHH, now i see the paper the OP was talking about Well spotted no idea how i missed that....and hmmmmmm

Yeah it would be too. I've seen plenty of arcade ones that didn't have the plastic but most of those had the CRT mounted on wood panels with no metal parts anywhere near the neck board.

You've probably already got your heart set on changing to a LCD but just want to mention that it's most likely that the CRT chassis just needs a little work, monitor is most likely still fine (especially if all the colour spectrum is still ok) I was advised by a pinball tech to keep the machine CRT if at all possible. There is a quite a debate about the advantages and disadvantages of CRT and LCD on these machines, it is of course a personal choice at the end of the day though.