  We show numerically that the response of simple amorphous solids (elastic
networks and particle packings) to a local force dipole is characterized by a
lengthscale $\ell_c$ that diverges as unjamming is approached as $\ell_c \sim
(z - 2d)^{-1/2}$, where $z \ge 2d$ is the mean coordination, and $d$ is the
spatial dimension, at odds with previous numerical claims. We also show how the
magnitude of the lengthscale $\ell_c$ is amplified by the presence of internal
stresses in the disordered solid. Our data suggests a divergence of $\ell_c\sim
(p_c-p)^{-1/4}$ with proximity to a critical internal stress $p_c$ at which
soft elastic modes become unstable.
