What is the ruling on money gained from winning an annual competition for website design, if the win was achieved through illegitimate means due to the manager's relationship with the evaluation committee, knowing that refusing to accept the money means it will go to the manager?

If the competition is permissible and lawful, then there is no objection to participating in it. However, if the manager is bribing the competition committee so that you win the prize, then this is forbidden and considered unlawful gain if it is highly probable that you do not deserve it. In this case, you must dispose of it by spending it on charitable causes. However, if these are mere doubts and delusions, then the prize is lawful. Money is not considered unlawful unless you are certain that its source is unlawful, and the default ruling is permissibility.