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Yes. You will get those points back if the late is deleted. Your score is based solely on what is on your report.
How long it will taken for all three bureaus to delete it is another story.
Any mortgage broker worth their salt can get that fixed for you, usually within a week's time. Be sure to provide the mortgage broker a copy of the bank's acknowledgment of their error; and the mortgage broker will send it in through their back channel with the credit bureaus, and this liaison will enforce what's commonly referred to as a Rapid Rescore.