All your income is taxable by your home state of GA, regardless of where you earn it. Therefore your employer is correct to withhold GA taxes.
As long as you do not physically work within Illinois, your income is not taxable by IL, even though your employer may be located there. Some states tax non-resident remote workers, but Illinois is not one of them.
Thanks for the reply- I came across this article can you take a look and let me know your thoughts?
https://www.thebalance.com/illinois-individual-state-income-tax-3193262
The Illinois Tax Rate
All residents and non-residents who receive income in the state must pay the state income tax. If you work in Illinois and live in any other state except Wisconsin, Iowa, Kentucky and Michigan, you must pay income tax to Illinois on any income you earn there. Illinois has reciprocity with those four states so residents can cross state lines to work without worrying about paying income tax to their non-resident state.
The Illinois state tax rate is 4.95 percent effective July 14, 2017. It was 3.75 percent prior to this date.
Here's a link to the actual Illinois law: http://www.ilga.gov/legislation/ilcs/ilcs4.asp?DocName=003500050HArt%2E+3&ActID=577&ChapterID=8&SeqStart=3100000&SeqEnd=4000000
Section 304 (a)(2)(B)(i and ii) state that "Compensation is paid in this state [and taxable by Illinois] if the Individual's service is performed entirely in this state"; or "both within and without this state".
If your service is performed entirely without (outside) Illinois, it is not taxable by Illinois.