Is it considered a sin to give the female Quran teacher additional hours for memorizing the Quran over the phone without the knowledge of the institute owner and without pay?

If the institute stipulates a fee for teaching female students seeking an Ijaza (a certification of Quranic recitation), or if this is the established custom, then it is obligatory to adhere to it, and it is not permissible to teach for free, as this would harm the institute. However, if this is not stipulated, and custom does not prevent free teaching outside agreed-upon working hours, then it is permissible for you to teach for free. It is preferable to seek permission from the administration because free teaching might financially harm the institute. There is no objection to teaching for free to correct recitation (tajwid) or for another program not affiliated with the institute.