The hole spectral function of the t-J model on a two-dimensional semi-infinite lattice is calculated using the spin-wave and non-crossing approximations. In the case of small hole concentrations and strong correlations, t >> J, several near-boundary site rows appear to be depleted of holes. The reason is a deformation of the magnon cloud, which surrounds the hole, near the boundary. The hole depletion leads to a more complicated spectral function in the boundary row in comparison with its bulk shape. This is connected with a maximum related to the underlying row, which reveals itself in the boundary spectrum.