You can, but it shouldn't be necessary to include this. What should happen is that that "income" is subtracted from Missouri taxable income. This is because it is a state refund. The IRS does not tax you when you receive a Federal refund, and the state does not tax you when you receive a state refund.
Since you are an Illinois resident, and Illinois taxes all of your income, if Illinois taxes another state's refund when you have itemized on the Federal Return in the previous year (and I don't think they do), whether you allocate the incme to Missouri or not won't matter for Illinois. But it won't be taxed in Missouri regardless.
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