You cannot directly reset or edit the game counters yourself, but you can manually trigger a recalculation.
Your officials' game counters automatically reset at the start of a "new season." That automatic recount will usually occur within 48 hours after creating your first assignment for the "new season." You can find the date of your "current season" above the grey navigation bar on the right-hand side of every page on the desktop/laptop system. If your "Current Season" is incorrect, you'll need to adjust your season start/end dates. This can be done in your System Settings under the System Defaults tab by adjusting your Season Start Month.
If you make changes to your Season start/end dates, it may take up to 48 hours to reflect the changes in your counters.