How could you fix a tv screen that's been touched with a magnet?

Answer Probably you can't. If the phosphor coating on the inside of the screen has been damaged, there is no way to repair it. A Cathode Ray Tube (CRT) is a sealed glass tube which is evacuated, which means that there is vacuum inside. There is no way to open the tube without breaking it.

Answer You'll need a "degaussing" coil. Basically it's a large magnet that you move around the front of the picture tube, and slowly move away from it. The procedure is simple, but without a good degaussing coil you can't really fix it.

The above comments, of course, only apply to older CRT-type TVs. Modern LCD screens are not affected by magnets and do not suffer from "phosphor burn".