Is it permissible to return the unjustly taken property to its owners—stolen money and a scratched car—without informing them of the doer, and how should one deal with a school principal who is not committed to returning what is due to him?

It is not a condition that those who have been wronged be informed of the return of what was wrongfully taken from them. Therefore, it is permissible to return it without their knowledge. What was mentioned about bearing the costs of repair and sending an apology letter to the school principal is a good deed that fulfills the purpose.