What does this mean igned arrears, retained by the State for TANF reimbursement?

If you are receiving "transitional istance" (formerly known as AFDC or "welfare") for your child, The state has subrogation rights to any court ordered child support and may therefore claim all or a portion of it as reimbursement for monies the state has given you for your child. I don't know how the amounts are calculated. It may have taken a couple of months for their systems to catch up with the fact that they would be deducting this.