Is it permissible to take old and damaged books from the workplace administration without the manager's knowledge, in exchange for waiving grants offered by the administration to the employee, after paying money for these books?

If the items are damaged and ready to be discarded, there is no objection to taking them and benefiting from them, with or without the manager's permission, because the company has relinquished them. However, if they are not in such a state, explicit permission from the administration is required. If they are for sale, their known price must be paid to the relevant party. It is not permissible for the price to be a waiver of grants unless there is mutual agreement and consent between the employee and the administration, for Allah Almighty says: "O you who have believed, do not consume one another's wealth unjustly but only [in lawful] business by mutual consent." Mutual consent requires knowledge of the price and the item, and the agreement of both parties to the exchange.