How can the relationship be repaired and trust be restored with the girl after threatening her with scandal due to adultery, and does God forgive the penitent who strives to please Him?

Adultery is one of the major sins forbidden by the Qur’an, the Sunnah (definition), and scholarly consensus. Its consequences are severe in this world and the Hereafter. A Muslim must repent from it by abandoning the sin, regretting it, and resolving never to return to it. The first duty of the one who repents is to distance himself from the girl with whom he committed adultery. Marrying her is not a condition for repentance or for rectifying what was corrupted. It is permissible for both of you if you both repent, but if she refuses, it is not permissible to compel her, and the duty is to avoid her.