  We propose an ansatz for encoding the physics of nonlocal spacetime defects
in the Green's functions for a scalar field theory defined on a causal set.
This allows us to numerically study the effects of nonlocal spacetime defects
on the discrete Feynman propagator of the theory defined on the causal set in
1+1 dimensions, and to compare to the defect-free limit. The latter approaches
the expected continuum result, on average, when the number of points becomes
large. When defects are present, two points with the same invariant spacetime
interval can have different propagation amplitudes, depending on whether the
propagation is between two ordinary spacetime points, two defects, or a defect
and an ordinary point. We show that a coarse-grained description that is only
sensitive to the average effect of the defects can be interpreted as a
defect-induced mass and wave-function renormalization of the scalar theory.
