If there are black spots in the LCD, 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.