Cleaning my Macbook screen *under* the shield
To do this the risk of further damage is rather high as I had to do this before on the same Mac. You will need a heat gun to heat the edge of the screen so you can pull it off then after it is separated you will need microfiber cloths and denatured alcohol (available in the paint section of any store) to wipe the LCD and glass cover perfectly clean. After finished you can use your glue of choice to put it back together however keep in mind pretty much any glue you use will not come back off without breaking something, so there is no turning back. Personally, either use an external screen or buy a new one off eBay (which is what I did). I found with mine it separated because the hinge cracked and wasn't able to tell this till after I opened it.