  A few dark matter substructures have recently been detected in strong
gravitational lenses though their perturbations of highly magnified images. We
derive a characteristic scale for lensing perturbations and show that this is
significantly larger than the perturber's Einstein radius. We show that the
perturber's projected mass enclosed within this radius, scaled by the log-slope
of the host galaxy's density profile, can be robustly inferred even if the
inferred density profile and tidal radius of the perturber are biased. We
demonstrate the validity of our analytic derivation by using several
gravitational lens simulations where the tidal radii and the inner log-slopes
of the density profile of the perturbing subhalo are allowed to vary. By
modeling these simulated data we find that our mass estimator, which we call
the effective subhalo lensing mass, is accurate to within about 10\% or smaller
in each case, whereas the inferred total subhalo mass can potentially be biased
by nearly an order of magnitude. We therefore recommend that the effective
subhalo lensing mass be reported in future lensing reconstructions, as this
will allow for a more accurate comparison with the results of dark matter
simulations.
