Am I permitted a financial reward—which is government money—that was disbursed based on assisting office staff in organizing a private charity party for the official's wife, and how should I dispose of it if it is unlawful and impossible to return to the state treasury?

If the official is authorized to act, then there is no blame upon you for benefiting from the reward. However, if the reward is specifically for those who helped at the ceremony, and you are not among them, then it is not permissible for you to benefit from it, and you must inform the director. If he grants you permission, then there is no blame. Otherwise, it is obligatory to return it to the state treasury. If that is not possible, then it should be given for the general benefit of Muslims or to the poor and needy.