My lawyer gets some advice about my case from her partner at her firm...

...A couple weeks later my lawyer leaves the firm and I go with her. My lawyer calls me from her new firm to give me heads up about the bill I'm going to get from her old firm. She says that the partner lawyer went into the billing system and charged me for an hour and half conversation. But that she really only had, at most, a half hour conversation. My lawyer advises me to not pay that portion of the bill and don't say anything and they'll forget about it. But I do say something. I email the partner explaining the situation. He emails back saying he had a very long conversations about my case and did extra research beyond the conversation and, in fact, did not charge me for all his time. I tell my lawyer what the the partner said and she says that was the worst thing you could have possibly done because now you called him out basically saying his dick was small.

Sow now is this a good plan of action? Pay the bill in full. I don't want any trouble with bill collectors or arbitration. And then email the partner saying, "Thank you for your explanation. I've paid the bill in full and I'm going to report the incident to the CA state bar." Does reporting the incident any weight? What can happen to the lawyers if I do that? Can my lawyer get in trouble somehow?