rent overlap - who keeps the money?

[George P.]

the tenant that's leaving paid until june 1 and moved out already. still has the keys and checks on the property regularly.

new tenant is moving in on 5/21. there is a 9 day overlap where i am double dipping.

i asked the current tenant for the keys and she said "will give it back on the 31st". i can easily change the locks/keys, but dont want it to become a big deal.

Do i owe her back the 9 days rent?