Why do I have to pay the full month of interest when refinancing an FHA loan if paid prior to the end of month?

I am refinancing my FHA mortgage to a conventional loan. My current lender requires that I pay interest until 03/01 even though the loan will be paid off a few days into February by the new lender. Essentially I will be paying interest to two lenders for most of February. I called the current lender and they stated it will not be refunded once the pay-off is received. Anyone know why this is and if there is any way around that?

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