It is possible for trust to be restored between those who have lost trust in each other, but it is much easier to lose trust than to build it again, and there is hard work involved in healing damaged trust. It is necessary first to acknowledge that trust has been damaged, and if there has been deception on the part of one party, then there must be full confession and acknowledgment of guilt. But Paul had not lied and he had been unjustly slandered by the Judaizers when they accused him of dishonesty. He must restore trust by reminding the Galatians that he had always conducted himself with honesty and so make them see that it was completely unjustified for them to harbour suspicions of him. It was they who needed to be ashamed not him.
As Luther says, If an apostle could come to the position where his integrity was questioned by his own converts, then certainly other ministers will face the same trial. It is indeed a painful trial when those who ought to be most loyal and convinced of our integrity, because they first heard the truth from our lips and believed to the saving of their souls, now begin to doubt that we are straightforward with them. Can they believe us for one thing and not another? Can they believe us for what is most important to their eternal welfare and not for a lesser matter? Paul had to re-establish his integrity before he could influence them by his teaching again.