put a delta on the tardy entry time
Recording the entry time is distracting. Say I know a student is 5 minutes late... how about I enter "5" in the "Minutes late/early" box. The computer could calculate the actual time (if anyone cares).
Isn't "5 minutes late" more useful to all parties than "arrived at 9:17"?
If it comes down to a court case, the day's schedule could be factored in.
I said "minutes late/early" because the same scheme could be used for Left Early"

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Smith, Flint commented
This isn't an either-or proposition. Two alternative entry methods could be accepted.
If the teacher prefers to enter 9:17 they could enter that in the "TIME" box. If they preferred to enter how late the student was, they could enter "5" in the "DELTA" box.
If only one is accepted, and you're the person choosing, imagine telling a Mom that their son arrived late at 9:17. What's the first question she'll ask? You know.
Is it that you only want one column to have the late information? Well, to that I say this: The absolute time data is useless in the future if you have not also collected the schedule at the specific school site on the specific date of the event. Was it a (PD) shortened tuesday? A minimum day? Without that, how do you know if 9:17 was 5 minutes late or 25?