Remove tenant with no current lease

[Carrie Nevins]

My tenant signed her one year lease in August 2019, set to expire August 2020. In August 2020 I asked if she'd like to continue living in the residence on a month to month tenancy and she agreed. I should note that she argued about the original lease being limited to one year and expressed that she'd like to stay at least 5 years. 

October 2021 we have decided to sell the house and gave her a 30 day notice to vacate on October 15. She asked for an extension on October 29 and we agreed to extend through December 1. During this time frame she called and asked "what do we have to do to let her stay in the house for four more years." She has also repeatedly told me that she can't find anything on the market. 

At any rate, she has stopped responding to me as of last week and hasn't communicated anything regarding the move out. Since she doesn't technically have a current lease I'm curious what my rights are? I've done a little reading and it seems like this is considered tresspassing and I will still have to get a court order from a judge to remove her with a sheriff present. 

Can anyone confirm this or offer any further details in this type of scenario? The residence is located in the state if Missouri. Thanks!