Hello again and thank you for your reply. I still don't see where you have asked a specific question, but I will assume that you are asking if you can force the employer to remove a warning from your file. There are only two ways that you might be able to have this warning removed from your file. The first, which you must do, since you work under a bargaining agreement, is to file a grievance. There is no work around that. That is the purpose of the union and the BA and if the union is refusing to file a grievance on your behalf, then you should consider speaking to a labor
attorney as you would likely have a suit against the union for bad faith and violation of their fiduciary duty to you as your representative.
The only other way that this could ever be removed, which would be somewhere down the line, would be if the employer shared this information with an outside party who was not privileged, for example a prospective employer, and a court concluded that the statement was a false statement of fact that the person making it knew or should have known was false when they made it. That would be defamation of character. However, at this point, since your employer has apparently not shared this with a 3rd party outside your company or a privileged party, that cause of action is not yet ripe.
So, again, the only way to get this removed in the short term is to grieve he warning and then if you lose the grievance to follow the next steps under the BA, which would be binding arbitration.
Please let me know if you need any clarification. I would be glad to assist you further if I can.