All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Dear inquirer! Know that marriage constitutes one of Allah's Signs and His sublime visible wisdom.
Allah, The Great and Almighty, Says: {And among His Signs is this, that He created for you wives from among yourselves, that you may find repose in them, and He has put between you affection and mercy. Verily, in that are indeed signs for a people who reflect.} [Quran 30:21]
Allah has also described marriage relations with ‘solemn covenant’, as He Says (what means): {But if you want to replace one wife with another and you have given one of them a great amount [in gifts], do not take [back] from it anything. Would you take it in injustice and manifest sin? And how could you take it while you have gone in unto each other and they have taken from you a solemn covenant?} [Quran 4:20-21]
Thus, the inquirer has to know that marriage ties are to be built on mercy and cordiality not on deceit and wrangling.
In addition, their behavior (his and his wife's) is contrary to sound conduct to be followed in accordance with cordiality and mutual trust.
Anyway, we advise you to be frank with your wife and to tell her that the cheque is still with you, so if she returns as a wife, then the problem is finished; otherwise, if she accepts to cede the cheque in return for divorcing her and you accept the cheque against your wife's bond of marriage, then it is up to you.
But, if you want to take the cheque in return for her requesting a divorce only, then this is not allowed; and it will be a form of taking the property of other people unjustly.
However, if she demands divorce, then she becomes recalcitrant (disobedient); and a wife in such a state is to be treated as stated in the Quran; Allah Says (what means): {But those [wives] from whom you fear arrogance - [first] advise them; [then if they persist], forsake them in bed; and [finally], strike them. But if they obey you [once more], seek no means against them. Indeed, Allah is ever Exalted and Grand.} [Quran 4:34]
As for taking her property as a first step of treating her, this in fact constitutes a violation to the teachings of Islam. In addition, a wife is not permitted to demand divorce if there is no genuine harm to her. Thawbaan narrated that the Prophet said: “Any woman who demands her husband to divorce her without a harm, she is forbidden to (smell) the fragrance of Paradise.” [At-Tirmithi and Abu Daawood]
For more benefit on the steps to be followed by the husband in dealing with a disobedient wife, please refer to Fataawa 89480, 84120, 357901, 85402, 400900, and 83244.
Allah knows best.