You remove it by telling TurboTax that the child lived with you 5 months or less.
You need to understand what you (and she) can and cannot do. To do that, you need to grasp the concept of custodial parent, for tax purposes. She did NOT (most likely) accidentally claim him for EIC. Even if she did, it is not optional, who claims EIC. That is, you cannot remove it from your return to allow her to claim it.
For tax purposes, there is no such thing as joint custody, regardless of what your legal agreement says. The requirement, to be custodial parent, is that the child live with you MORE than 50% of the time. One of you has to be the custodial parent and the other the non-custodial parent. The IRS goes by physical custody, not legal custody.
