What is the optimal action regarding a financial reward that was mistakenly disbursed to a student and then returned, with the intention of expiating the mistake and negligence? And is it permissible to purchase Qur'ans with it and dedicate them as an endowment (waqf) in the school?

The amount that was mistakenly disbursed must be returned to the student rewards budget so that it can be spent for its intended purpose. It should not be spent on purchasing Qur'ans or anything else; rather, it must be returned to the rewards item. You must strive, be cautious, and not be lenient in spending the money entrusted to you, for Allah Almighty says: "O you who have believed, do not betray Allah and the Messenger or betray your trusts while you know [the consequence]."