I'm not familiar with the display in question, but in general, the back is easily removable, while the tube is mounted on the front of the case, if this goes for the ADC display, I'd leave it dirty, removing the tube is a very risky business, the tube is where all the charge is (not capacitors, though there are nasty ones in a monitor, they should lose their charge within a day or so.)
If the dust is loose though, you should buy an air duster, it will easily blow out any dust that might be in there, and it comes in handy for cleaning dust from cards, and power supplies, etc.