What is the ruling of Islamic law regarding demanding the return of a portion of the father's inheritance to the sister, after it was agreed that she would relinquish her share in exchange for a car from the inheritance, then the car was returned, resulting in a financial loss?

If it was agreed that the sister would take the car in exchange for her share of the inheritance, this is permissible and is called "قسمة التراضي" (division by mutual consent). This division is binding and cannot be revoked.

So, if you did not agree to return the car after the agreement, the loss is borne by the one who returned it, because he disposed of his property. However, if you agreed to the return, the loss is on everyone, and the partners must bear the sister's share of the inheritance after distributing the losses.

Therefore, the sister must be given her right, while observing the fulfillment of rights and maintaining kinship ties.