  A microscopic approach is developed to scattering of surface states from a
non-magnetic linear defect at a surface with strong spin-orbit interaction.
Spin-selective reflection resonances in scattering of Rashba-split surface
states by an atomic stripe are theoretically discovered in a proof-of-principle
calculation for a model crystal potential. Spin-filtering properties of such
linear defects are analyzed within an envelope-function formalism for a
perturbed surface based on the Rashba Hamiltonian. The continuous Rashba model
is found to be in full accord with the microscopic theory, which reveals the
essential physics behind the scattering resonance. The spin-dependent
reflection suggests a novel mechanism to manipulate spins on the nanoscale.
