Ruling on reconciliation along with denial

Answer: What appears to me regarding this issue is that reconciliation along with denial is permissible, likewise reconciliation along with mutual admission of the disputed right, and also along with the right being clear to the judge. That is because the Lawgiver has urged excellence, forbearance, pardon and doing good. “And do not forget graciousness between you.” [al-Baqarah:237] and: “But indeed, whoever is patient and forgives – indeed, that is of the matters [requiring] resolve.” [al-Shūrā:43].
Ruling strictly by the right is only when separation [between them] becomes impossible except by that, and when the two disputants insist upon pure strict right and their souls do not accept forbearance. The Prophet (May Allah bless him and his family and grant them peace) saw a man clinging to another because of a debt, demanding its payment from him, so he (May Allah bless him and his family and grant them peace) gestured to the creditor to take half of his debt and remit the other half; the man agreed – this is the meaning of the narration.
And in the story of the trial (muḥākamah) between al-Zubayr and the Anṣārī in the presence of the Prophet (May Allah bless him and his family and grant them peace) there is that which indicates the permissibility of reconciliation even when the right has become clear to the judge. Likewise, what is in the story of the reconciliation of Sawdah with the Prophet (May Allah bless him and his family and grant them peace), for she, in that reconciliation, gave up a right that was firmly hers, and he (May Allah bless him and his family and grant them peace) in turn gave up a firm right of his that Allah had permitted him – namely, divorce.
Yes, the ḥadīth: “Reconciliation is permissible between Muslims except for a reconciliation that makes lawful what is unlawful or makes unlawful what is lawful” does not include what we have mentioned, for nothing in it makes lawful the unlawful or makes unlawful the lawful.
For the owner of a right may relinquish to his opponent or to someone else his right or his property, or some of either; and the opponent may give from his wealth whatever he wishes to whom he wishes, whether an opponent or someone else. There is nothing in that of forbidding what Allah has permitted or permitting what He has forbidden.
And reconciliation in such a manner does not make any unlawful thing lawful nor make any lawful thing unlawful; rather, it is an encouragement to perform acts of beneficence and graciousness, which are better than strict contention and mutual obstinacy. In it is safety from grudges and rancour, and in it is resolving the dispute without there being, in that, a victor and a vanquished, a conqueror and the conquered.
It is customary that the one against whom judgment is passed suffers a shock that is followed by grudges and rancour against the judge and against the one in whose favour judgment has been given. From this came the saying of Shurayḥ: “I awake each morning while half the people are angry with me.” In light of what we have mentioned, it becomes clear that reconciliation is better and more virtuous in such cases.
By this, the weakness of the statement of the scholars of the madhhab on this issue is also made evident, and its weakness is further borne witness to by what we observe – as you have mentioned – of the reconciliations that scholars effect between people in situations of denial; and praise be to Allah, Lord of the worlds.

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2