You got some REALLY BAD ADVICE.
You cannot remove the acetone. You have melted the plastic on the back of the screen. Acetone is a solvent for plastic.
If the area is very lightly affected, you may be able to hide the damage by using CAR BODY PASTE WAX as you would on a fine car finish. Car paste wax in a LIGHT application will fill the microscopically small pits in the plastic finish. Buffing the wax will probably make the dark finish on the back of the monitor look practically new.
The wax finish will not be as durable as the original plastic. Since it will sit facing away from viewers, it probably won't be noticed if you don't mention it. Car wax is tough and it should last as long as the monitor does.
You might have to buy a new case for the monitor or replace the whole monitor if your favour isn't appreciated by whomever you did this for.