"And give the women their dowries with a good heart..." [Noble Quran 4:4]
"...So for that pleasure which you have enjoyed from them, give them their prescribed compensation.. " [Noble Quran 4:24]
As you can see, the first part of the surah Allah (SWT), states to "Give the women their dowries with a good heart", meaning the said (Dowry Is already paid to the women In question).
"...All others have been made lawful for you provided you seek (them in marriage) with your property..." [Noble Quran 4:24]
Understand that "This Is a commandment from Allah (SWT)", when Allah (SWT) states "And give the women their dowries with a good heart...", this Isn't a request (It's not as If) Allah (SWT) stated "If you want to give them or not" but HE/Allah (SWT) stated "And give the women their dowries with a good heart".
That should be the end of the discussion (As for what, that women does afterwards shouldn't be your concern) as you already (Divorced her). Yet lets continue (For the sake of the question).
"...So for that pleasure which you have enjoyed from them, give them their prescribed compensation.. " [Noble Quran 4:24]
The next Ayat Allah (SWT) states the reason as to why (You/The Husband) have to pay this "Dowry" and the reason being Is because of the "Pleasure which you have enjoyed from them" and for the said "Pleasure" Allah (SWT) states "Give them their prescribed compensation" In this case (Dowry) that Is theirs to keep.
SAHIH INTERNATIONAL
Divorce is twice. Then, either keep [her] in an acceptable manner or release [her] with good treatment. And it is not lawful for you to take anything of what you have given them unless both fear that they will not be able to keep [within] the limits of Allah . But if you fear that they will not keep [within] the limits of Allah, then there is no blame upon either of them concerning that by which she ransoms herself. These are the limits of Allah, so do not transgress them. And whoever transgresses the limits of Allah - it is those who are the wrongdoers. 2:229
Again, I'd say that's pretty cut and dry (But with limited understanding of such matters) I read the Quran for that which It Is. Also, why do you really wish to "Tempt the wrath and punishment of Allah (SWT) for monetary things? Money comes and goes (That's life) but you've given this (Dowry) to a women, whom, you were married to at one point correct? Than you went onto that women+That women did do the house-hold chores and cooked and cleaned and took care of your needs, be In (Mental/Physical/Emotional and ETC) and she was a companion to you (At one point), so why would you wish to "Harm her), even "If she changed Religions"? That Is a matter for "her and Allah (SWT)" not "You and her and Alllah (SWT)".
And Allah Knows best but that Is the my answer to the question (Hope this helped).