It doesn't seem possible that the plate could rub against the points. It would have to hit the stator plate coils (primary ignition and lighting coils) first. But anyway, the thin plates are glued to the magnet core inside the flywheel, no screws. I would consider finding a new (used) one rather than trying to re-glue it. I would also expect to see other damage upon removing the flywheel if that plate came off with the engine running.
If you can't find a flywheel elsewhere, I will sell one for $10 plus shipping. You may well find one cheaper though.