What is the ruling on excess money that was mistakenly given to a person in a monthly installment, and then the person died, and their family returned the excess amount? Is this money lawful or unlawful?

If what you were given is the amount of increase over the agreed installment value that was mistakenly expended, then there is no harm in that. This is because this increase is rightfully yours, based on the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions concerning what is permissible." It is a condition for the permissibility of installment sales that the price be fixed, the installments known, the term specified, and that there be no interest charged for delays in paying installments.