I have a coworker (A) who brought to my attention that one of our mutual colleagues (B) told someone else that I was a "bad boss" and dishonestly refered to Coworker A as the one who told him (Coworker B) that statement. Coworker denies making any statement of that sort about me to anyone, much less to Coworker B. I don't mind receiving any constructive criticism about how I do my work but in this case coworker B dishonestly said that it was CoWorker A who told him such observation. I plan to file a grievance report vs Coworker B. Is that the right thing to do? How would you react if you were in my position?
[Edited to add]
Appreciate all the comments. Let me put into context the whole issue. Coworker B used to be the supervisor of CoWorker A until I came into the picture. And with the reorganizing in the office, coworker A returns under Coworker B. And CoWorker B has a pattern for making statements allegedly said by others to make his point and appears to mAke himself look good by making others look bad.and he would say, "according to Mr. x, mr Y is this..." Even if Mr. x when confronted never said those words. I was able to talk to Coworker A who personally told me that he told Coworker B that what he said about me which supposedly Coworker A said is not true. He insisted before Coworker B that he never made such statemnts and that for Coworker B to quote him in that was wrong.