  There is plenty of evidence in the literature of significant discrepancies
between the observations and models of metal-poor red giant branch stars, in
particular regarding the effective temperature, teff, scale. We revisit the
benchmark star HD 122563 using the most recent observations from Gaia Data
Release 3, to investigate if these new constraints may help in resolving this
discrepancy. We review the most recent spectroscopic determinations of the
metallicity of HD 122563 [Fe/H], and provide a new assessment of its
fundamental parameters, i.e. bolometric luminosity, teff, surface gravity, plus
a photometric determination of its metal content. Using these constraints, we
compare the position of the star in the Hertzsprung-Russell (H-R) diagram with
various recent sets of stellar evolution tracks. The H-R diagram analysis
reveals a significant disagreement between observed and theoretical teff
values, when adopting the most recent spectroscopic estimate of [Fe/H]. On the
other hand, by using the photometric determination of [Fe/H] some of the
selected sets of stellar tracks appear in fair agreement with observations. The
sets with discrepant teff can be made to agree with observations either by
modifying the prescription adopted to calculate the models' outer boundary
conditions, and/or by reducing the adopted value of the mixing length parameter
with respect to the solar-calibration. A definitive assessment of whether the
teff scale of metal-poor stellar red giant branch models is consistent with
observations requires an even more accurate determination of the fundamental
parameters of HD 122563 and also a larger sample of calibrators. From the
theoretical side, it is crucial to minimise the current uncertainties in the
treatment (boundary conditions, temperature gradient) of the outer layers of
stellar models with convective envelopes.
