What is the lawful right of a woman who has been divorced with a major irrevocable divorce, after agreeing upon a certain dowry, then registering a different dowry in the contract?

What is obligatory upon you is the dowry agreed upon secretly, not what was formally written down during the عقد (marriage contract) to spare the feelings of the family. This is based on the Almighty’s saying: "And give women their dowries as a free gift. But if they give up willingly to you anything of it, then take it in satisfaction and ease." (Quran 4:4). And act upon the secret dowry if we declare a different one.