What is the ruling and expiation concerning a wife returning to her husband after he divorced her with a minor irrevocable divorce (baynunah sughra) without a new marriage contract and a new dower?

A distinction must be made between them until a lawful marriage contract is concluded with her, fulfilling the conditions and pillars of marriage. His returning to her after a minor divorce (baynunah sughra) is considered an invalid return (raj'ah batilah), and they must repent and seek forgiveness for this sin.