  A non-relativistic scalar particle moving on a curved surface undergoes a
geometric scattering whose behavior is sensitive to the theoretically ambiguous
values of the intrinsic and extrinsic curvature coefficients entering the
expression for the quantum Hamiltonian operator. This suggests using the
scattering data to settle the ambiguity in the definition of the Hamiltonian.
It has recently been shown that the inclusion of point defects on the surface
enhances the geometric scattering effects. We perform a detailed study of the
geometric scattering phenomenon in the presence of line defects for the case
that the particle is confined to move on a Gaussian bump and the defect(s) are
modeled by delta-function potentials supported on a line or a set of parallel
lines normal to the scattering axis. In contrast to a surface having point
defects, the scattering phenomenon associated with this system is generically
geometric in nature in the sense that for a flat surface the scattering
amplitude vanishes for all scattering angles $\theta$ except $\theta=\theta_0$
and $\pi-\theta_0$, where $\theta_0$ is the angle of incidence. We show that
the presence of the line defects amplifies the geometric scattering due to the
Gaussian bump. This amplification effect is particularly strong when the center
of the bump is placed between two line defects.
