What should a woman who has done that do to atone for her sin, as she believes she was the reason the girl did not get married?

What the woman did by opening a letter that did not belong to her and withholding it from its owner is a reprehensible and forbidden act. She must offer sincere repentance to Allah and try to rectify the situation by informing the young man that the letter did not reach his fiancée so he can send another one, and by informing the fiancée of what happened and asking for forgiveness from everyone. However, if doing so would lead to a greater evil, then she should seek forgiveness generally without going into details.