The monitor is made of two layers of film - polarized and anti-glare. Take you box cutter blade and cut along the edges of the monitor to remove the films. Peel off the frosted anti-glare coating because it's not needed. Same goes for the polarized film, but save a piece because it's the secret ingredient to making this hack possible.
Next, get your paint thinner, or any other solvent, to soften the adhesive that remains on the glass. You may need to experiment with solvents and methods, however the user who came up with this idea, dimovi, suggests putting paper towels on the screen, soaking them in paint thinner and letting them sit. After you're done scraping the glue off with plastic or wood, reassemble the monitor.