Is the salary lawful if the employee's name was not included in the summer eyeglasses schedule due to an oversight by the responsible employee, and can the money be purified by donating the equivalent of one week's salary or by volunteering to work for one week?

If you strongly believe that your name was mistakenly omitted from the list of those entitled to receive spectacles, and that they are essential for your job, you must contact the administration to rectify the error or work for a week to compensate for the cost of the spectacles. It is not permissible for you to take money for a week you did not work, due to the generality of Allah Almighty's saying: "O you who have believed, fulfill [your] contracts," and His saying: "Indeed, Allah commands you to render trusts to whom they are due."