Praise be to Allah.
If he has indeed divorced her by khula’, in the sense that the marriage has been annulled and there is nothing left to be done except handing over the compensation (i.e., the mahr), then he has no choice in the matter, even if he has not yet taken back the mahr. But if they have agreed to khula’ without yet having the marriage annulled, rather they have agreed that he will let her go when she hands over the mahr, then this does not mean that the marriage has been annulled, rather it is promise to annul it. So if it has not yet been annulled, then he has the right to change his mind and not do that which he had intended. If he had said, “If you give me the mahr you will be free (I will give you khula’),” then according to the Hanbali madhhab he does not have the right to change his mind. But according to Shaykh al-Islam Ibn Taymiyah, if he has not yet taken back the mahr then he has the right to change his mind. In order to be on the safe side, if the latter scenario has taken place and they want to get back together, they should make a new marriage contract so as to put themselves beyond any area of scholarly dispute.