Acts 16:35
"And when it was day, the magistrates sent the serjeants, saying, Let those men go."
The magistrates made a mistake with Paul and Silas by imprisoning them on hearsay. They mistakenly followed the accusations of the mob, and sent soldiers to have them openly arrested. The problem was that the next morning they realized their mistake and wanted to privately release Paul and Silas. Paul's response was, "They have beaten us openly uncondemned, being Romans, and have cast us into prison; and now do they thrust us out privily? nay verily; but let them come themselves and fetch us out." Paul wanted the same people who arrested them openly to release them in open view so the city understood the mistake.
There are times when someone makes a mistake about a person and later they realized their mistake, but the damage has already been done. Whether you said something that was not true about someone or openly prejudged someone, it can damage someone's reputation for life if you don't properly handle your mistake. The incident with Paul and Silas teaches us what to do when we realize our mistake.
First, don't deny your mistake. Don't try to coverup your mistake for the sake of saving your reputation. When coverups are revealed, it can be worse than the admission of the mistake. People will forgive you if you show them that you made an honest mistake and truly plan on never doing that again. When a mistake has been made, admit it even if you are the leader and it may temporarily hurt your credibility. You will save the confidence of those who follow you when they see that you are willing to admit and correct your mistakes.
Second, be as open about your apology as you were about your mistake. Paul made it clear that because he was arrested publicly that he should be released publicly. Don't try to do a back page apology when you are wrong. You need to be as public about your apology as you were about your mistake to help rebuild the credibility of those whose reputation you hurt.
Third, don't punish the offended to save your reputation. Sadly, the magistrates wanted Paul and Silas to quietly leave town so their reputation wouldn't be damaged. The person whose reputation you hurt has already been punished enough by your actions, don't add to it by asking them to move on to save your reputation. If you are honest about correcting your mistake, then both of you will be able to dwell together.
Let me caution you to be careful with accusation. Once you accuse someone of something, you will never be able to stop the chain of conversations that hurt that person. Just like you can't gather all the feathers of a feather pillow that's been opened, you will never be able to completely reverse the damage you made to someone whom you attacked. Your attack against a person will always leave questions to others minds about that person.
Learn to withhold accusations just because you dislike someone or you suspect someone. The best way to treat others with accusations or suspicion is to treat them the same way you would want to be treated if you were in their shoes. Someday, you will be in their shoes, so do the right thing with others and you will have fewer regrets later in life.