All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the husband had uttered the Khul’ or divorce on the condition that the wife will give him back the dowry, then separation between them took place and the husband cannot take her back except with a new contract.
However, if the husband did not utter the words of Khul’ or divorce, then according to the most preponderant opinion of the scholars separation does not take place just by the wife giving back the dowry to the husband. So, she is still his wife and he is not obliged to divorce her. However, if she hates him, then it is desirable for him to accept to give Khul’ to her but if they reconcile and the wife is pleased to stay with him, then the bond of marriage is still valid and there is no need for a new marriage contract.
Allaah Knows best.