  A nonrelativistic scalar particle that is constrained to move on an
asymptotically flat curved surface undergoes a geometric scattering that is
sensitive to the mean and Gaussian curvatures of the surface. A careful study
of possible realizations of this phenomenon in typical condensed matter systems
requires dealing with the presence of defects. We examine the effect of
delta-function point defects residing on a curved surface ${S}$. In particular,
we solve the scattering problem for a multi-delta-function potential in plane,
which requires a proper regularization of divergent terms entering its
scattering amplitude, and include the effects of nontrivial geometry of ${S}$
by treating it as a perturbation of the plane. This allows us to obtain
analytic expressions for the geometric scattering amplitude for a surface
consisting of one or more Gaussian bumps. In general the presence of the
delta-function defects enhances the geometric scattering effects.
