Quick answer
A private agreement may not change a court order or the agency’s accounting.
Do now
Save the agreement and all payment evidence. Ask how to submit a consent modification for court approval. Confirm whether any money is owed to a public agency and whether both parents can legally compromise it. Use traceable payments through the ordered method.
Watch for
Gifts, groceries, and payments outside the official channel may not receive the credit you expect. Do not assume a parent can permanently waive a child’s support rights.
Official sources
NJ Courts — FD modification application packet, NY Courts — Starting a Child Support Case, DC Courts — Parentage and Child Support Branch.