Do I Need To Pay Arrearages On My Child Support Case

I recently gave my 2 children up for adoption. My ex-wife's husband adopted them, therefore the child support order stopped. The problem I have is that my ex- wife signed a notarized paper stating she would forgive the arrearages. Child support states that they don't recognize that paper as a legal document. They sent her a paper to sign, which she isn't going to, to forgive all the arrearages. She also verbally agreed, telling child support she would forgive the arrearages. Do I have to pay the arrearages since I have that notarized paper with her signature on it, stating she would forgive the arrearages? Please help