Unless I’m missing something, the landlady doesn’t know what she’s talking about. Quite clearly says, at the end of paragraph 3, “if and extension is required for a few days than the daily rate shall be calculated by dividing the monthly rent by 30.5 days”
If you stay an extra day, you pay one day’s rent.
I wouldn’t pay her anything other than the one day and I would point that clause in the rental agreement to her and ask you to explain how she thinks you therefore owe her one month.
Can I clarify anything else for you?
I’m happy to answer any specific points arising from this.
Please take a moment to look at the top right hand corner of the page and rate my service by clicking one of the stars at the top of the screen. It’s important you use the rating service because that gives me credit. It doesn’t just give me a pat on the head! (Although there is an incentive scheme where the more five-star ratings I get, I do actually get a pat on the head! :-)) All you need to do is press Submit. Thank you.
If you still need any point clarifying, I will still reply because the thread does not close.