My mom got her Social Security check on the 3rd she died on the 28th, my dad had to pay it back. Was that correct?

Why are you worrying about something that happened 23 years ago?

Your Social Security works just like a job. You get paid after u do the work. So if the check was received Oct 3 it was for September. She died in September so is not entitled to that check.

By the way, this was all explained to me when I signed up for SS.

Yes he did. Dad would have had to pay even if Mom got her check on the 1st and died on the 31st. That's the rule.

Yes as she didn’t live for the entire month before. The 3rd of the month payment was for prior month.
IF this is truly about a transaction from 1997?!?!, this is so sooooo long ago it doesn’t matter even if there was a mistake.