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Some CC issuers do mid-cycle updates when specific events occur. For example, some Chase cards update balances if you pay it down to zero. Moreover, some CC issuers like US Bank report at specific times (end of month for US Bank) and not around the statement cut date. Many banks report within a few days of the statement date, but not all do.
Also, in your case a off-cycle update may have occured to remove the late. If the late and the utilization change were on the same card, both might have been updated. The only way to say for sure is to pull your report. Unfortunately, myFICO will not alert you when a late is removed and a score recalculation won't occur unless a triggering event takes place.
A new late is a triggering event for an alert and a score recalculation, but a removal of a late is not to the best of my knowledge. For example, if the late is removed tomorrow, your score won't recalculate until another triggering event like a balance change occurs. When the new triggering event occurs, myFICO will notify you of the triggering event only and recalculate your score taking into account both triggering events (like a balance change) and non-triggering events (like a removal of a late). It is possible that your issuer reported both in an off-cycle update and myFICO triggered a recalculation due to the balance change but took into account both.
Finally, a 36 point change could be just for utilization or for both. It comes down to your current score and profile. The lower your score, the more likely it factored both, but if your score is near 700 or so, chances are it is only one of the two causing the change. Simply put, negatives hurt a lot more when you have a higher score. If your score is 800+, a 30 day late could drop you a 100 points, but if your score is 550 or so, it won't usually hurt too much. Again, this is not exact since the FICO formulas are proprietary and the impact of any one category or event varies based on your overall profile. But as a general rule, the higher your score the more the impact of negatives.