You're in GA....I'm in Ga..unless laws have changed, I would think same applies to you.
Back in 90's similar payment of 1400.00 happened to me. I had a lawyer buddy on speed dial.
Anyhow answer is NO, you do not have to pay it back. Of course being worried a bit I ask him to expound further.
''If they had any legal grounds, they would have had a judgement against you [me] and they would have attached your checking/savings what ever liquid assets you have. They don''t have any ground to stand on other than forcibly ask you return they moola"
Once paid they can't get it back, unless in your case their is some clause in your severance package specifically stating they could. In that case you can assume they would have referenced said clause in letter sent to you.
After a second letter sent to me I replied back: Further contact regarding this matter should be sent to my attorney & supplied his address. Never heard from them again.
Edit:
10 years ago my insurance Co. said they overpaid my claim by 640.00, according to them, what I got did not fully cover the loss,just weeks later they "demanded" repayment.
I kept it and told them politely go pound salt, once again they had no legal ground to stand on. No my homeowners policy did not go up, nor did they cancel me. The only recourse either instance they had, would have been to cancel the check before it was cashed & re-issue another one in correct amount. Apparently this has been 'tested' in court.