Lump sum severance- pay back?

So my last day is in a week and I will be receiving a lump sum severance. I am interviewing for part time positions tho at the company. Would I have to pay it back if they re-hire me? Odds are they won’t be able to make anything happen in a week so if in a month they find something what happens to that lump sum? The part time role would pay less than my current role too so not sure if that plays into it. My severance agreement didn’t mention anything aboit clawbacks or rehire etc. thanks!