English Explanation of Mishnah Sanhedrin 6:6

When the flesh was completely decomposed, the bones were gathered and buried in their proper place.
The relatives then came and greeted the judges and witnesses, as if to say, we have no [ill feelings] against you, for you gave a true judgment.
And they observed no mourning rites but grieved [for him], for grief is in the heart alone.
Mishnah six discusses the process which occurs a year or so after the initial burial of the criminal. At this time formal reconciliation is made between the family of the criminal and the court, thereby restoring proper order to society.
When the flesh was decomposed the bones were allowed to be returned to their ancestral burial place. This is the first step of reconciliation: allowing the criminal’s bones to rejoin the bones of his family. The mishnah then prescribes a procedure in which the relatives of the criminal were to greet the judges and witnesses, thereby tacitly admitting that the verdict had been correct. This second process of reconciliation and admission to the authority of the court allows society to return to some sense of normalcy, after the severe disruption of an execution. Finally, although the family may not observe proper mourning rites, which would involve elaborate eulogies and public rituals, inappropriate for a criminal, they were allowed to observe the private ritual of grief. While the mishnah cannot allow the public ritual, it is sensitive to the private needs of the mourning family. This too is a form of reconciliation, as if the court is saying to the family that although your relative was a criminal, the moral stain is not borne by his entire surviving family. They are to return to regular members of society.