Is the sale of my mother's plot of land, through a mediator who profited 2,400 dinars without her knowledge, Islamically permissible, and is it permissible for the mediator to take this amount, and does any sin fall upon my mother as a result?

If a mother authorizes someone to sell her land, and he sells it for more than the price she told him, and he keeps the excess for himself, then he must return the excess to the mother. This is because an agent is a trustee, and he must act in the best interest of the principal. Taking the excess is a betrayal and an unlawful appropriation of money, as indicated by the Hadith (definition) of Urwah al-Bariqi. If the mother absolves him of the excess, that is permissible. However, if she tells him: "Sell it for 115 dinars, and whatever is extra is yours," then the excess becomes his fee, and he is entitled to it.