Is the money taken for covering up someone who was found in an unlawful private meeting permissible? And if it is not permissible, what should be done with it?

The young man and woman should have been denounced and warned of Allah's wrath. Reaching a settlement with the young man and taking money in exchange for covering up for him is impermissible. It is a form of consuming people's wealth unjustly, because a settlement requires that what is being settled over be a right belonging to the one settling. Exposing the young man or bringing his matter to court is not a right. The money must be returned to its owner. If that is not possible, then it must be given as charity on his behalf for charitable causes and public welfare.