Does the mother retain custody of her daughters after remarrying, given that her ex-husband had in writing relinquished custody to her in exchange for her waiving her mahr?

"Khul' (divorce at the instance of the wife) is valid through the wife's relinquishing all or part of her mahr (dowry), or by compensating with more than it. If separation occurs between the spouses, whether by divorce or khul', the mother has the primary right to custody of her young children as long as she does not remarry. If she remarries, her right to custody is forfeited. Scholars have differed on whether custody is a right for the custodian or the child. The correct view is that it is a right for the child and a duty upon the custodian if the child needs it and no one else is available. If both parties agree to transfer it, it is permissible. It is permissible for the father to relinquish his right to custody to the mother, even for compensation. However, the best interest and right of the child in custody must be considered. If the relinquishment would lead to the neglect of the child's right, then custody would be taken from her."