The ex is only allowed to claim her if you give them permission by giving them a signed form 8332. This is assuming that you are the custodial parent (the one with whom the child lived with the most nights). Should you give them the dependency, you can still file as Head of Household using that child and can also claim child care credit and EIC if otherwise qualified. The other parent only gets child tax credit.
Having written the above, your settlement gave the other parent the dependency and if you use IRS rules to avoid that, it is then a civil matter for the court to enforce. The IRS pays no attention to divorce agreements.
