Is what the questioner did forbidden, and is the money he earned throughout this period forbidden, knowing that the daily wage is calculated via this card?

If the employee is present during official working hours and performs the tasks assigned to them, then their salary is lawful (halal (definition)). They are entitled to the wage simply by making themselves available for work during its appointed time. It is permissible to request the card if signing with it is common practice, provided that the request comes from the person in charge of it and is done in a legal manner that does not necessitate lying or deception. One must adhere to labor laws and regulations and refer to those authorized in such matters.