Teleworking in Georgia, moved to Texas

I have been teleworking in Georgia 1.5 years for a major corporation where my assigned office is located a 100+ miles away. I have only gone into work once last year and once this year.  I can continue working the same job and moved to Texas (no official state tax; however, state collects taxes via property ownership at 3% value of house, which is similar amount to the Georgia State income tax).  I suspect even though my permanent residence is in Texas, unless I get my company to change my work address to an office in Texas, I will continue paying Ga State Income tax on top of my Texas property tax, is this correct?

 

If so, what classification must I request my company change me to? 
Remote working instead of Telework, or is the only way I will not pay Georgia State Tax is re-assign me to an office in Texas or take another job?

 

TIA for the answer!