Pay on the 15th

They wouldn’t have any grounds to foreclose if they received the money by the fifteenth.  That’s what a grace period means.  You’d be trashing your credit record, of course, if you did that regularly.

Simply mailing your check on the fifteenth, though,  wouldn’t do it. The payment would reach your lender after the grace period expired.  Your loan would be in default, leaving you in danger of foreclosure.