Is it permissible to agree with the seller to increase the price of the remaining quarter of the property so that this increase can be reclaimed from the seller and paid as a down payment to the bank, knowing that this does not affect the financing amount, profits, or installments?

This is not permissible because it involves deception and fraud against the bank, and it includes usury (riba) due to the accrued interest on the increase. The sin falls upon both the buyer and the seller who cooperate in this act. As for the bank, it is not held accountable due to its ignorance of the true nature of the matter. Therefore, beware of this forbidden act. For whoever fears Allah, He will make for him a way out and provide for him from where he does not expect.