How do I locate the date that I set up for my Illinois taxes to be paid

[Critter]

Check the printout or PDF of your return; look for the state cover sheet with the Turbotax logo.  

If you owed tax, they will show the payment information and how you decided to pay.  This is the same info that was posted on the screen that you must have missed reading ....

> If you  owed  the state   ... read the state payment instructions carefully since most states cannot be paid from within the TT system and requires additional steps.   https://ttlc.intuit.com/questions/1900884-what-are-my-options-for-getting-my-state-refund-or-for-pay...