Are the doubts surrounding the validity of the employee's action in reducing the price of the books justified, and is what she did considered fraud against the school and its owner?

The basic principle is that an employee is entrusted with their work. So, if it is possible to verify with the authority responsible for the system of giving books for free or at a reduced price, then that is excellent. Otherwise, pay the price of the books to the relevant authority if it becomes clear that there was deception or fraud. Otherwise, there is no sin, and دفع الشبهة أولى (warding off doubt is more prudent).