Drop a name in Registry from Possession Documents

Hi All I had purchased a property in the name of my Father and Mother i.e. the possession letter and other builder documents is in both their names. Now since my father had in his name some capital gain from LTCG, my CA suggested him to get registry done in his name if he wants to take the tax benefit of Section 54 for full amount, else if the property is registered in both the names, then the benefit he can get is only 50% and the other 50% will go to my mother's name and will be wasted. To do this, we asked our builder to do so, for which he is asking handsome amount to change all his documents. Someone in my known told me since 1 name has to be dropped, it can be done using NOC / Affidavit from my mother. Please advise what is the legal way of doing this. New Property is located in Haryana. Old Property was sold in UP. Regards Harshit