  While most moving groups are young and nearby, a small number have been
identified in the Galactic halo. Understanding the origin and evolution of
these groups is an important piece of reconstructing the formation history of
the halo. Here we report on our analysis of three putative halo moving groups:
G03-37, G18-39, and G21-22. Based on Gaia EDR3 data, the stars associated with
each group show some scatter in velocity (e.g., Toomre diagram) and integrals
of motion (energy, angular momentum) spaces, counter to expectations of
moving-group stars. We choose the best candidate of the three groups, G21-22,
for follow-up chemical analysis based on high-resolution spectroscopy of six
presumptive members. Using a new Python code that uses a Bayesian method to
self-consistently propagate uncertainties from stellar atmosphere solutions in
calculating individual abundances and spectral synthesis, we derive the
abundances of $\alpha$- (Mg, Si, Ca, Ti), Fe-peak (Cr, Sc, Mn, Fe, Ni), odd-$Z$
(Na, Al, V), and neutron-capture (Ba, Eu) elements for each star. We find that
the G21-22 stars are not chemically homogeneous. Based on the kinematic
analysis for all three groups and the chemical analysis for G21-22, we conclude
the three are not genuine moving groups. The case for G21-22 demonstrates the
benefit of combining kinematic and chemical information in identifying conatal
populations when either alone may be insufficient. Comparing the integrals of
motion and velocities of the six G21-22 stars with those of known structures in
the halo, we tentatively associate them with the Gaia-Enceladus accretion
event.
