If you have a Georgian office paying Georgian salaries for the work that produced export services, then I don't see a reason for Georgian banks to have a problem, even if the owners and customers are offshore.
If the work is done offshore, the customers are offshore and the owners are offshore, then Georgian banks are less likely to be interested in that business.
Georgia has "virtual zone companies". Same tax concept as Estonia - no CIT until dividends are paid out, and only 5% in that case.
So it should be possible to have a company in Georgia, be a resident of Estonia and pay only 5% tax on dividends that are paid out.
Surely this could be taxed as an Estonian PE, unless the work is done and managed in Georgia? Or is there a DTA loophole?