Question how to remove this dirt on my monitor?

Try a good quality screen cleaner fluid.

Rather than spray the cleaner fluid directly on to the screen, spray it on to a microfibre cloth then wipe the screen with the cloth.
This will avoid the risk of fluid running down in to the monitor through the bezel at the bottom.
 
Make your own cleaning solution by mixing distilled water (make sure it’s distilled) and white vinegarin equal proportions into a spray bottle. Turn off your laptop. Spray this mixture lightly onto the microfiber cloth, not onto the monitor. Wipe the screen in circular motions. Be gentle, but apply slight pressure on particularly stubborn spots.