Thanks for letting me know that you're using the Enterprise version and sharing the on-point details about your concern, @cericha. 

Changing your State Unemployment Insurance (SUI) rate in the program automatically adjusts your liability amounts for Q1 and Q2. It could be the liabilities were paid outside QuickBooks but were not entered in the software, that's why the system doesn't recognize the credit.

I've got some steps to help you get rid of the overdue check from the Payroll Center window. This can be done by entering a prior tax payment for Q2 to mark it as paid. Then, choose Do not affect accounts since your liability balances and A/P balances are already accurate. Let me guide you how. 

1. Go to Help from the top menu and select About QuickBooks Desktop Enterprise.
2. On your keyboard, press Ctrl + Alt + Y to open the Setup YTD Amounts window.
3. Choose Next until you reach the Enter prior payments section.
4. Click Create Payment.
5. Enter the Payment Date and For Period Ending date accordingly. 
6. In the Taxes and Liabilities field, choose the SUI tax and then enter the amount.
7. Click the Accounts Affected button.
8. Choose Do not affect accounts, then click OK. 
9. Click Done.
10. Hit Finish to close the window.

The screenshot below shows you the fourth to eight steps. For more information, see the The Liabilities were paid but never entered into Desktop section through this article: Scheduled Liabilities Payroll Show As Overdue or In Red. 

January is one of the most important months for every business, just like yours. You can visit this website: Year-end Checklist. This link contains essential dates and tasks to help you start and complete the year-end payroll process. 

I'm just a post away if you need anything else. Have a good day, @cericha.