Does cleaning the back of the MacBook lid damage the front of the screen at all if the lid is open?

I would never clean it with the display open as it is too easy to accidentally damage it. When cleaning the external parts, close the lid and gently wipe them making sure to only lightly dampen the microfiber cloth.

When I clean the glass, I will open the display and place the back of the display on a flat surface with the keyboard/palmrest standing up in the air. This way I can easily wipe the display glass without worrying about any twisting of the screen which could cause damage. It is hard to clean the glass while also trying to hold it in place since it tends to bounce and even twist....both of which could potentially cause damage. With the laptop open and sitting on the display as described it provides a steady surface to wipe, but you must be careful not to press too hard or it will damage the glass and/or LCD Panel. Avoid pressing on the glass Bezel at the bottom of the Display which has the "MacBook" name as this glass Bezel is very fragile & easily damaged since most of the area beneath the Bezel is hollow or has mylar flex cables so the Bezel has no support beneath it.

Hello! Congratulation on your new Mac! If you are cleaning it gently while open, this shouldn't be a big problem but it is better to do it while the lid is closed. It shouldn't make any difference if the computer is on or not, but it is better if it is off. Enjoy using your MacBook Pro! If you have more questions, don't hesitate to ask. Have a nice day!