  We investigate factorized scattering from a reflecting and transmitting
impurity. Bulk scattering is non trivial, provided that the bulk scattering
matrix depends separately on the spectral parameters of the colliding
particles, and not only on their difference. We show that a specific extension
of a boundary algebra encodes the underlying scattering theory. The total
scattering operator is constructed in this framework and shown to be unitary.
