The eminent Muslim scholar and renowned Da`iyah, Sheikh `Abdel Khaliq Hasan Ash-Shareef, states: “Majority of Muslim scholars are of the opinion that a woman in her menses is not allowed to enter the mosque. However, a group of Muslim jurists hold the opinion that it is permissible for a menstruating woman to enter the mosque on condition that she preserves the purity of the mosque and the menstrual blood does not fall in the mosque. According to some scholars, it is also permissible for a menstruating woman to attend a lecture in the mosque.
Given the above, it becomes clear that there is nothing wrong for menstruating women to sit and eat in the mosque with fasting Muslims on condition that they try their best to keep the mosque clean.