Weak G-band stars, or carbon-deficient red giants (CDGs), are a rare class of chemically peculiar G and K giants with carbon abundances that are under-abundant by about a factor of 20 when compared to that of the normal giants. Despite their discovery nearly 70 years ago, the origin of carbon deficiency remains a puzzle. We aimed to better characterize the CDGs by using asteroseismology (Kepler, TESS), spectroscopy (APOGEE, LAMOST), and astrometry (Gaia). We identified 15 new CDGs in the Kepler field and, for the first time, unambiguously identified their evolutionary state as being in the red-clump phase. Our findings reveal that CDGs are primarily low-mass stars (M ≤ 2.0 M⊙), unlike previous suggestions of them being intermediate-mass stars (2.5−5.0 M⊙) based on the HR diagram. The demarcations in chemical patterns and luminosities led us to categorize them into three groups. We concluded that a merger of a helium white dwarf with a red-giant branch star is the most likely scenario for the two groups of over-luminous stars. For the normal-luminosity CDGs, we could not distinguish between core He-flash pollution or lower-mass merger scenarios. The strong correlation between CDGs and Li-rich giants suggests a potential link between their formation processes.