Tenant wants prorated rent without proper notice

[Jane Robinson]

Hi everyone, I have a situation with my tenant that I'd love the BP community perspective on. Own a property in MT that my husband and I bought with a tenant in place about 3 years ago. When we took possession we had her sign a month to month lease with 30 days notice. She always knew that our intention was to move into the property eventually. 

We are finally in a position to move into the property and gave her notice on Dec 10 for end of January. Since it was over the holidays and with covid we wanted to give her some extra time to find a place. She responded to the email saying she was shocked and upset, so we told her we could be flexible if she really needed a later date. We agreed that she would start looking and she would keep us posted on move out date. She has been a good tenant and paid on time. 

Fast forward to Jan 6 and she said she has found a place, will be moving out Jan 16 and wants us to refund prorated rent for January. I'm pretty sure that we are not required to refund any rent given she only gave 10 days notice. I'm thinking we keep the rent for January and call it even. Am I missing anything here?

Thanks!