Is the examination and approval by a manager of commissions and gratuities given by sales representatives to customers considered participation in sin? And are these commissions permissible in Islamic law?

It is necessary to know who the clients are to whom commissions are paid. If they are buyers or authorized agents who are permitted to receive commissions, then there is no objection to paying them with the permission of an authorized person. However, if the clients are agents who are not authorized to take commissions for themselves, or if the commissions are paid to nullify a right or to uphold falsehood, then these commissions are prohibited bribery, and it is forbidden to give or receive them. Assisting in such bribes by examining or approving them is not permissible, due to the Almighty's saying: "And do not cooperate in sin and aggression." This applies if the examiner knows it is a bribe; but if he does not know, then there is no sin upon him, and he is not obligated to inquire.