What is the ruling on forgetting to pay Zakat al-Fitr and remembering it after the Eid prayer, knowing that the family paid it on behalf of the entire household?

Zakat al-Fitr is obligatory upon you from your wealth. It is a financial act of worship that requires intention, so it is not valid unless you pay it on your own behalf or authorize someone to pay it for you. This is because if your family pays it on your behalf without your knowledge, it is not valid. You must pay it as a make-up payment (qada'), because it is a debt upon you that is not waived by the passage of time.