  The measured emission-weighted metal abundance of the hot gas in early-type
galaxies has been known to be lower than theoretical expectations for 20 years.
In addition, both X-ray luminosity and metal abundance vary significantly among
galaxies of similar optical luminosities. This suggests some missing factors in
the galaxy evolution process, especially the metal enrichment process. With
{\it Chandra} and {\it XMM-Newton}, we studied 32 early-type galaxies (kT
$\lesssim$ 1 keV) covering a span of two orders of $L_{X,\rm gas}/L_{K}$ to
investigate these missing factors. Contrary to previous studies that X-ray
faint galaxies show extremely low Fe abundance ($\sim 0.1$ Z${_\odot}$), nearly
all galaxies in our sample show an Fe abundance at least 0.3 Z${_\odot}$,
although the measured Fe abundance difference between X-ray faint and X-ray
bright galaxies remains remarkable. We investigated whether this dichotomy of
hot gas Fe abundances can be related to the dilution of hot gas by mixing with
cold gas. With a subset of 24 galaxies in this sample, we find that there is
virtually no correlation between hot gas Fe abundances and their atomic gas
content, which disproves the scenario that the low metal abundance of X-ray
faint galaxies might be a result of the dilution of the remaining hot gas by
pristine atomic gas. In contrast, we demonstrate a negative correlation between
the measured hot gas Fe abundance and the ratio of molecular gas mass to hot
gas mass, although it is unclear what is responsible for this apparent
anti-correlation. We discuss several possibilities including that externally
originated molecular gas might be able to dilute the hot gas metal content.
