Forgiving Back Child Support Arrears

My husband has a child with another woman. The woman's husband would like to adopt the child. My husband is agreeable to this. The mother mailed us paperwork to have signed and notarized to give up his parental rights. We understand that this will eliminate any further child support accumulation. However we are hesitant to return the paperwork because it did not address his back child support owed. The mother is agreeable to forgiving the arrears. How do we take care of this? Can we add a statement to the relinquishment of parental rights paperwork she sent us, sign and notarize it, to take care of this issue? Thank you for your help in this matter.