Is the interest in a mortgage payment for last month or next month?

I’m in the process of refinancing and I have a question about the breakdown of the typical mortgage payment. The amount required to payoff the old loan does not match the amortization schedule.

I made my last payment on February 1st. I did not make the March 1st payment because the closing is set for March 3rd.

They are telling me that I need to pay the interest for the month of February. Please explain.

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