Creation and annihilation of point-potentials using Moutard-type transform in spectral variable

We continue to develop the method for creation and annihilation of contour singularities in the $\bar\partial$--spectral data for the two-dimensional Schrödinger equation at fixed energy. Our method is based on the Moutard-type transforms for generalized analytic functions. In this note we show that this approach successfully works for point potentials.