Is it considered wrong to rebuke a girl asking for help in front of the mosque in an inappropriate way, specifically when recalling Allah's saying: "And as for the one who asks, do not repel [him]"?

There is no harm in admonishing a child to stop an action that might harm him or others. Indeed, the Prophet, may Allah's prayers and peace be upon him, admonished Al-Hasan ibn Ali, may Allah be pleased with them both, when he took a date from the dates of charity, saying: "Kakh Kakh." As for the verse, "And as for the beggar, do not repel [him]," it specifically prohibits admonishing a needy beggar.