Cumulative eccentricity (e₂) distribution of the tertiary orbit of CHTs listed in Table D.1. Left: Cumulative e₂ distribution of CHTs of different [fe/H] values. Yellow represents metal-rich samples, red represents solar ones, and purple represents metal-poor ones. Right: Cumulative e₂ distribution for young (blue) and old (red) systems. The black line represents the expected trend for a flat distribution and the dashed green line is the expected trend for a thermal distribution of e₂. The grey lines in both panels show the total distribution of all the listed CHTs.