Is it permissible for an employee to take compensation for extra effort exerted outside the scope of their contract and working hours, without the knowledge of the company, which threatened to dismiss them if they did not perform this work?

The questioner has a right to demand payment from the employer for work performed outside the scope of the contract. If he finds no way to receive what is rightfully his except by taking the money without the employer's knowledge, then there is a difference of opinion on this matter. However, the fatwa among us permits this, provided that he takes only what is due to him, without any excess.