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 _c that diverges as unjamming is approached as _c ∼ (z − 2d)^−1/2, where z ≥ 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 _c is amplified by the presence of internal stresses in the disordered solid. Our data suggests a divergence of _c ∼ (p_c − p)^−1/4 with proximity to a critical internal stress p_c at which soft elastic modes become unstable.