IRS Publication 504 page 13 addresses Alimony payments. 

https://www.irs.gov/pub/irs-pdf/p504.pdf

It does not specify if a "Repayment" of Alimony would be deductible or not so it may depend on your interpretation of page 13 rules. 

Based on the publication this would not be reported on the Schedule A, it is normally deducted on the 1040 Schedule 1 line 31a. 

Since this is reported on the 1040 as a deduction that would reduce the Federal AGI and IL uses the Federal AGI as the starting point to determine the IL Taxable income any Alimony Paid would flow to IL as part of the Federal AGI for line 1.