There are cases (black spot on the screen, screen only works for half the digits, broken screen) where the only solution is to change the screen. These are not produced anymore, so you will need to find a donor HP41c.
To replace the screen: First unsolder the two screens (from the donor and the damaged calculator) Use a small soldering gun and help lifting the pins with the tip of a plier, one by one. Important: unsolder the screen at the calculator side: it is much more resistant!!!
Then solder the donor screen back in place. Locate the screen in its hole first. then start soldering pins, with a very clean soldering gun. There is no need to add more solder. After melting the solder, leave the gun while maintaining pressure on the pin with a flat screwdriver tip, to ensure good, durable contact. Patience until finished. Then reassemble and try again.