If the heirs of the buyer accepted the amount their deceased paid as the price for the house, does Islamic law obligate returning the original value of the amount, or its equivalent in gold at the present time?

If there is evidence that the deceased purchased the house, then the house belongs to the heirs, even if there is no official contract. The seller has no right to take the house or demand a refund of the price, and he should not be indulged in that. Nevertheless, there is no harm in agreeing with him on compensation in exchange for returning the house to him. The seller should know that a court ruling in his favor does not make it permissible for him to take the house, because the Prophet, peace and blessings be upon him, said: "You come to me with your disputes, and perhaps some of you are more eloquent in presenting their case than others. So, if I rule in favor of someone concerning the right of his brother based on what he says, then I am only cutting off a piece of hellfire for him, so he should not take it."