  The Gaia DR3 GSP-Spec parameters, including metallicity, for VMP stars suffer
from parameter degeneracy due to a lack of information in their spectra.
Furthermore, the recommended quality cuts filter out the majority of the VMP
stars because some of them are confused with hot stars or cool K and M-type
giants. We aim to provide more precise metallicity estimates for VMP stars
analysed by the GSP-Spec module by taking photometric information into account
in the analysis. We reanalyzed FGK type stars in the GSP-Spec catalog by
computing the Ca triplet equivalent widths from the published set of GSP-Spec
stellar parameters. We compare these recovered equivalent widths with the
values directly measured from public Gaia RVS spectra and investigate the
precision of the recovered values and the parameter range in which the
recovered values are reliable. We then convert the recovered equivalent widths
to metallicities adopting photometric temperatures and surface gravities. The
recovered equivalent widths agree with the directly measured values with a
scatter of 0.05 dex for the stars that pass the GSP-Spec quality cuts. At the
low metallicity end ([Fe/H]$<-1.5$), our metallicity estimates have a typical
uncertainty of 0.18 dex, which is about half of the quoted GSP-Spec metallicity
uncertainty at the same metallicity. Our metallicities also show better
agreement with the high-resolution literature values than the original GSP-Spec
metallicities at low metallicity. While the GSP-Spec metallicities show
increasing scatter when misidentified ``hot'' stars and the subsets of the
``cool K and M-type giants'' are included, we can now identify them as FGK-type
stars and provide metallicities that show a small scatter in the comparisons.
Thanks to the recovery of these originally misclassified stars, we increase the
number of VMP stars with reliable metallicity by a factor of $2-3$.
