Is it permissible to marry a girl with a bad past, and should I continue to invite her to return to her religion and repent, especially if she had worn the hijab and then abandoned it?

Your da'wah to that girl was a mistake. It would be more appropriate to invite her through your sisters or maharim (unmarriageable kin), for the tribulation of women is great and dangerous. A righteous man can be tempted by a single glance. Therefore, we advise you to turn away from her and to seek out righteous women to invite her.

As for marrying her, if you are certain or it is highly probable that her condition will change for the better, towards righteousness, uprightness, and adherence to Islamic dress, then your marriage to her is praiseworthy, for you will be a cause for her guidance, and this is better than red camels.

However, if you know that she is not sincere in her claim, then we do not advise you to marry her, especially if your parents are not pleased and her reputation is not good.