He cannot claim the EITC if he is the non custodial parent. The only credit he can claim as the noncustodial parent is the Child Tax Credit. So he will need to remove that credit from his return.
In the personal info section, did you select that you had an agreement with the other parent to claim your child? If not, then you will need to Amend Your Return to remove the Child Tax Credit by saying the other parent will claim them this year. The Amended forms are not yet available for the year. He will then need to mail in his return because your return will take up to 4 months to process, then you would need to repay the $2,000 per child tax credit (or however much you received per child that he was to get)
You can also just pay him the amount that you are getting for the kids if you are getting a large refund. That would be easier for both of you. However, if he makes more or vice versa, one of you may see a bigger difference on their return than the other did on theirs.
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