  Quiescent galaxies at $z \gtrsim 2$ are compact and have weak or absent
emission lines, making it difficult to spatially resolve their kinematics and
stellar populations using ground-based spectroscopy. Gravitationally lensed
examples provide a promising route forward, but such objects are very rare. We
describe a search in the fields of 232 galaxy clusters that has uncovered five
bright ($H_{\rm AB} < 20$) lensed galaxies with red near-infrared colors. These
include MRG-M0138, the brightest lensed galaxy known in the near-infrared.
Analysis of near-infrared spectra and multiband photometry confirms that all
are quiescent galaxies at z=1.95-2.64 with stellar ages of 0.5-1.4 Gyr
(corresponding to formation epochs $z_{\rm form} \simeq 3-4$) and stellar
masses of $10^{11.6-12.8} \mu^{-1} M_{\odot}$, where $\mu$ is the
magnification. In three cases we derive lens models and reconstruct the source
structure; these galaxies are massive ($M_* \gtrsim 10^{11.0} M_{\odot}$) and
follow the mass--size relation defined by unlensed samples. In two of these
three galaxies, the main structural component is an inclined disk. Weak
emission lines are detected in four of five galaxies with high ratios
[NII]/H$\alpha$~2-6 that are inconsistent with a star formation origin. Based
on the line ratios, the H$\alpha$ equivalent widths, and the distribution and
kinematics of the gas, we infer that shocks are likely present in at least two
galaxies and could be present in all of the line emitters. We speculate that
these could be analogs of local galaxies in which AGN jet-driven outflows are
thought to heat the interstellar medium and suppress star formation. In further
papers we will present spatially resolved measurements of the stellar
populations and kinematics of this unique sample.
