Does a woman who has been irrevocably divorced through Khulʿ return to her husband merely by his secluding himself with her during the waiting period, or does that require a new contract and a new dower?

So long as the husband divorced his wife in return for absolution (ibra’), then his divorce is a final, irrevocable (bain) divorce. He cannot take her back except with a new contract and a new mahr. Therefore, it is not permissible for her to obey him in secluding herself with him or in conjugal relations, because he is a stranger to her.