  We demonstrate that the perturbations of strongly lensed images by low-mass
dark matter subhalos are significantly impacted by the concentration of the
perturbing subhalo. For subhalo concentrations expected in $\Lambda$CDM,
significant constraints on the concentration can be obtained at HST resolution
for subhalos with masses larger than about $10^{10}M_\odot$. Constraints are
also possible for lower mass subhalos, if their concentrations are higher than
the expected scatter in CDM. We also find that the concentration of lower mass
perturbers down to $\sim 10^8M_\odot$ can be well-constrained with a resolution
of $\sim 0.01''$, which is achievable with long-baseline interferometry.
Subhalo concentration also plays a critical role in the detectability of a
perturbation, such that only high concentration perturbers with mass $\lesssim
10^9M_\odot$ are likely to be detected at HST resolution. If scatter in the
$\Lambda$CDM mass-concentration relation is not accounted for during lens
modeling, the inferred subhalo mass can be biased by up to a factor of 3(6) for
subhalos of mass $10^9 M_\odot$($10^{10} M_\odot$); this bias can be eliminated
if one varies both mass and concentration during lens fitting. Alternatively,
one may robustly infer the projected mass within the subhalo's perturbation
radius, defined by its distance to the critical curve of the lens being
perturbed. With a sufficient number of detections, these strategies will make
it possible to constrain the halo mass-concentration relation at low masses in
addition to the mass function, offering a probe of dark matter physics as well
as the small-scale primordial power spectrum.
