Yep, you took a union job.
Not filing the grievence was the right move, don't stir the pot. But it sounds like someone doesn't like you. They jumped right to the harshest punishment.
You know you can't change jobs there, so you might just as well start looking elsewhere. If you find a new postion, but they want you to stay, you insist that the letter get removed. If they don't, move on. my $.02