Tenant over-payment of last months rent

[Garen T.]

I have a tenant on a month-to-month lease. I collected 1st and last at lease signing. She has been there for 18 months. 

August 1, right on time I get a payment from her. 

August 2, she sends a text giving notice. She wants to move out during 3rd week of August and is fine paying for the full month. Is asking for a refund of the (now) Sept rent she paid 18 months ago. She has been a decent tenant, and I'm not expecting any damage or cleaining fee. I paid for a cleaning crew prior to her moving in, and then she hired another one to clean my clean SFR.

I wish she hadn't paid me yesterday, but is there any valid reason for not doing the refund of the last month rent? I'm not sure the whole point now of why collect it to begin with. 

Thoughts?

[Peter M.]

Don't refund anything until she is out. Period.