How to Unring a Bell

Is it possible to “unring” a bell?
My first attorney in New York argued long ago it was not possible to “unring” a bell once it had been rung.
He explained to me how, in law school, he was taught the first thing you learn in open court is if your client “rings a bell” — that is, says something incriminating or stupid or wrong — you must not draw attention to it by “ringing” that bell again.

“Once the bell is rung,” he would say, “there’s no way to unring it, so ignore it and move along.”
Does “unringing a bell” have resonance beyond a Big Box O’ Justice to find reverberation in our ordinary lives?
If we say something wrong or make a big public mistake — do we apologize and make amends — or is it better to just “move along” without stopping to sound the gaffe again and then try to silently to fix the error with positive future action?
Can a bell be “unrung” or not?