Is it permissible for a private school to disburse to the guardian the surplus from checks it received from charities to cover his son's tuition fees, if these checks exceed the determined fees?

So long as the checks are specifically for tuition fees, the guardian is not permitted to use them except for this particular benefit. If any amount remains from them, he is obliged to return it to the granting entity or seek their permission to use it for another purpose. If you knew that these checks were issued exclusively for this purpose, and you had already covered the fees from other sources, then you are not allowed to cash them. If you do cash them and there is any surplus amount remaining, it must be returned to its owners or their permission must be sought for its disposal.