Is it impermissible to agree to deduct a certain amount from the carpenter due to poor paintwork, and then for the paintwork not to be fixed and to remain as is, especially since the carpenter claimed injustice?

If experts determine that the painting is defective and estimate the cost of its repair, then there is no harm in deducting this amount from the carpenter, and you are not obligated to spend it on the painting, and there is no injustice to the carpenter in that. You are entitled to compensation. Jurists have affirmed the option of defect for the mustasni' (one who commissions manufacturing). If the manufacturer cannot rectify the defect, the mustasni' has the right to demand a replacement or terminate the contract. It is permissible to agree on compensation for the deficiency. If you voluntarily give the carpenter a portion of the amount, you will be rewarded for it.