Did not file IL State tax return in 2020. Owed no tax. Letter from IDOR says I have till Friday to respond. I did the State return on Turbo ta. Can I file it now from Turbo tax?

A 2020 tax return cannot be e-filed.  The only way to file a 2020 return is by mail.   If you prepared your 2020 federal return using TurboTax then you can use the CD/download software on a full PC or Mac to prepare a 2020 state return.  

https://ttlc.intuit.com/questions/1900990-how-do-i-file-a-prior-year-tax-return

You can use TurboTax to prepare the 2020 state income tax return - but as it is a prior year return, you will not be able to electronically file the return. Rather, you will need to print and mail the return to the state.

I recommend using certified mail. I also recommend calling the state (often the state notices will have a contact number listed), and let them know you are sending the completed return in.  The letter may also have a fax number where you can fax the return to instead of mailing.