I just have to keep telling myself this happens in other businesses, just so I won’t explode

on Tuesday, I told the TL that was taking the piss when she was off on Friday but it always feels like she defends him. She said he starts at 9. I said no, he starts at 9 when in the office because he couldn’t make the 8am starts, then couldn’t make it when it got moved to 8.30, so it got moved to 8.45 and it finally got moved to 9am because he was always late! I corrected her and said she told me he does 8-5 when wfh. Then she started wittering on about the school run. I said it was half term last week, so there was no school run on Friday (where we live).
It sounds petty to moan about it, but I value fairness and consistency and my line manager just doesn’t care.