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.
Khul' is seeking divorce in return for compensation, so if a woman asks for divorce and the husband was not the cause for her asking divorce, then he is permitted to take a compensation for divorcing her, which is something agreed upon between them. Therefore, if you agreed with your wife for this compensation to be what you called the dowry items, then it is permissible for you to take that, otherwise it remains her property.
The following matters should be mentioned:
1- A woman is not permitted to leave her husband's house without his permission. If she does so without any valid reason, then she is a disobedient wife.
2- A wife is not permitted to ask for divorce except for a religious reason.
3- Divorce leads to serious consequences on the family, especially if the spouses have children. It is for this reason that whenever reconciliation is possible, one should resort to it. Allaah Says (what means): {… and settlement is best.}[Quran 4:128].