  We report a search for excess absorption in the 1083.2 nm line of ortho
(triplet) helium during transits of TOI-1807b and TOI-2076b, 1.25 and
2.5R$_{\rm Earth}$ planets on 0.55- and 10.4-day orbits around nearby
$\sim$200~Myr-old K dwarf stars. We limit the equivalent width of any
transit-associated absorption to $<$4 and $<$8 mA, respectively. We limit the
escape of solar-composition atmospheres from TOI-1807b and TOI-2076b to
$\lesssim$1 and $\lesssim$0.1M$_{\rm Earth}$ Gyr$^{-1}$, respectively,
depending on wind temperature. The absence of a H/He signature for TOI-1807b is
consistent with a measurement of mass indicating a rocky body and the
prediction by a hydrodynamic model that any H-dominated atmosphere would be
unstable and already have been lost. Differential spectra obtained during the
transit of TOI-2076b contain a He I-like feature, but this closely resembles
the stellar line and extends beyond the transit interval. Until additional
transits are observed, we suspect this to be the result of variation in the
stellar He I line produced by rotation of active regions and/or flaring on the
young, active host star. Non-detection of escape could mean that TOI-2076b is
more massive than expected, the star is less EUV-luminous, the models
overestimate escape, or the planet has a H/He-poor atmosphere that is primarily
molecules such as H$_2$O. Photochemical models of planetary winds predict a
semi-major axis at which triplet He I observations are most sensitive to mass
loss: TOI-2076b orbits near this optimum. Future surveys could use a distance
criterion to increase the yield of detections.
