  We devise a test of nonlinear departures from general relativity (GR) using
time delays in strong gravitational lenses. We use a phenomenological model of
gravitational screening as a step discontinuity in the measure of curvature per
unit mass, at a radius $\Lambda$. The resulting slip between two scalar
gravitational potentials leads to a shift in the apparent positions and time
delays of lensed sources, relative to the GR predictions, of size $\gamma_{\rm
PN}-1$. As a proof of principle, we use measurements of two lenses,
RXJ1121-1231 and B1608+656, to constrain deviations from GR to be below
$|\gamma_{\rm PN}-1| \leq 0.2 \times (\Lambda/100\, \rm kpc)$. These
constraints are complementary to other current probes, and are the tightest in
the range $\Lambda=10-200$ kpc, showing that future measurements of
strong-lensing time delays have great promise to seek departures from general
relativity on kpc-Mpc scales.
