The standard scenario for the production of carbon-enhanced extremely metal-poor (CEMP) stars requires a more massive binary companion, which has evolved through the AGB stage and transferred carbon-rich material to the surface of the surviving, likewise extremely metal-poor (EMP) star. Evidently, the binary companion plays a key role in this process.
In order to characterise the polluting star, if any, the stage of evolution of the observed star (whether RGB or AGB), and whether pulsations exist, must be known. The Gaia DR2 parallaxes and photometry should contain the answer.