High q-resolution neutron-scattering measurements of the critical scattering in Tb above the magnetic-spiral phase transition temperature T(s) exhibit a two-component line shape, as recently documented in Ho. This implies the existence of a second length scale. By using a narrow beam only 300 mum wide, and then translating the crystal through the beam, we have established that the origin of the second length scale lies within the near-surface volume or ''skin'' of the Tb crystal. This is manifested by a large enhancement of the scattering intensity at the c-axis face of the cube-shaped crystal.