Tech support may have been suspicious of the package you describe, because it is indeed suspicious. Each InterLink is sold as part of a package along with the software. They should be sold together or not at all, whether new or used.
RealFlight G3 shipped with the InterLink Plus. The InterLink Elite was not available until RealFlight G4 or later.
That's why the situation you describe doesn't add up. You should have received an InterLink Plus to go with that G3 software, or else the purchase should have been for a later version of the software to go with that InterLink Elite. Mixing and matching isn't allowed and doesn't make sense. In this case, somebody somewhere must be missing an InterLink Elite that they need.
At any rate, there's nothing you can do to make G3 work with that InterLink Elite. There is no workaround. But as others have said, you can purchase the RealFlight 6.5 upgrade.