...... Several years ago there was a payroll system enhancement that eliminated the taxing issues.
In the past, green checks were issued outside of the payroll system. The next week, the wages associated with that check would need to be added to the QTD and YTD wage and tax totals in the payroll system. It would get added to your current week's wages which sometimes increased the gross wages enough to trigger a slightly higher tax rate. Payroll was supposed to manually control the taxes which meant calculating the taxes on the green check and calculating the taxes on the current check then overriding the payroll system to match those totals.
Now, green checks are issued through the payroll system as a stand alone check and are not added together with the current week's payroll. In fact, if it's only a partial week payment, such as a missing day or a rate adjustment, the taxes will be lighter than if it was included on your regular paycheck because of the lower gross wage amount.