They find their way in between the LCD/TFT panel and the mirror via the grills on the back of the screen, pests!. They are really small bugs, known as thunderbugs as well, that suck the juices from leaves, probably a millimetre long.
I was lucky last year and didn't have to remove any.
The two I found have vacated but it's really annoying when you see them crawling around inside your monitor.