Lavery told Woolf in an email these comments allowed readers to infer the council unreasonably pursued the matter, which "couldn't be further from the truth", and could be read as criticisms of officers involved.
"The staff involved have been distressed by those comments and your involvement in the matter. I feel that I have no option but to raise this directly with the mayor."
Former mayor Justin Lester sent the investigation in motion on the cusp of last year's local body elections.
A lawyer was engaged, who started requesting information from relevant parties, but it's unclear how far this process progressed.
New mayor Andy Foster has been reluctant to pursue the matter and Lavery has repetitively declined to comment.
It's understood Woolf was presented with a deal that if he apologised and accepted that he had breached the council's code of conduct, the independent investigation would be shelved.
But Foster said following correspondence with Woolf, he's satisfied a line could be drawn under the whole thing.
"He's [Woolf"] accepted that he has said things that he should not have said, he's accepted also that those things have caused distress to some staff, and he has given an undertaking that those sort of things will not happen again."
Foster also wanted to avoid the cost of such an inquiry.
"Which frankly probably would have had very little real outcome", he said.
Woolf said it was a huge relief.
"There's been a lot of angst, especially during the election period. I'm just rapt that common sense has taken place really."
Woolf maintained he never breached the council's code of conduct but admitted he could have handled things better.
"I will just be careful as to the way that I comment on issues.
"In this situation there was no intent to upset people in a direct sense, it was more regarding policy and procedures, it wasn't aimed at one personality or another."
