Is it permissible to take an additional sum of money disbursed by mistake, in order to compensate for previous work for which payment was not received?

If you received an excess amount by mistake, you must refer to the entity that disbursed it. If it was with their knowledge and consent, there is no blame. However, if it was by mistake, and if both entities share the same financial budget, then it is permissible to take what compensates your right from the other entity if it cannot be obtained through normal means. This is the Madhhab Al-Zafar (the view permitting a wronged person to take their right by force if unable to obtain it otherwise). But if the two entities do not share the same budget, then it is not permissible to take the additional amount, because the injustice done to a person does not permit them to wrong others.