What are the rights of a woman who is divorced through khul'?

The opinion implemented in Egypt by law and fatwa is as follows:

Based on the opinion of some scholars on this issue, when the courts grant a woman divorce through khul' [divorce initiated by the wife in return for remuneration to her husband] she is to return to him the mahr [dowry] she received.

Registry of furnishings

The registry of furnishings is a wife's civil right that is similar to a debt which a husband owes to his wife. If there is nothing in the registry of furniture to indicate that all or part of it constitute the mahr, then it is the wife's exclusive right whether or not she is divorced through khul'; she does not have to give back the articles included in the registry of furnishings after khul'.

However, a wife must return to her husband any item mentioned in the registry of furnishings which constitutes the mahr, since in this case it is not considered a debt but a compensation in return for divorce.
God the Almighty knows best.