Is it permissible for the heirs to demand compensation for a plot of land that was added to the sales contract after their grandfather's death, knowing that it is adjacent to the sold land and has no other neighbors? And what should the mother do if the rest of the heirs insist on not relinquishing their claim?

If the second plot of land was originally your property and you did not bestow it upon the buyer, then you may sell it with a new contract. However, if it was barren land (ard mawat) that the buyer revived through cultivation and construction, then it has become his property, and you are not permitted to sell it. If some of the heirs insist on not waiving their rights, the mother can waive her right to the plot in favor of the buyer to clear her conscience.