Is it permissible to take a percentage from the price difference between what the client was informed of and the actual price, given that the broker is aware of the buyer's authorization based on the reported price, and is this act considered brokerage?

You must inform the agent of company (B) of the real price, and that it is not permissible for him to take the price difference without the knowledge and consent of company (A) which commissioned him to purchase. He must explain the truth of the matter to company (A). For an agent only acts within the scope of what he has been authorized to do, as evidenced by the hadith (definition) of Urwa ibn al-Ja'd al-Bariqi. Furthermore, the real price must be recorded in the invoices and not falsified. Brokerage is permissible provided it is with the knowledge and consent of the one from whom it is taken; otherwise, it is consuming wealth unjustly, which is among the major sins.