Linear theory for phonon scattering by discrete breathers in the discrete nonlinear Schrödinger equation using the transfer matrix approach is presented. Transmission and reflection coefficients are obtained as a function of the wave vector of the input phonon. The occurrence of a nonzero transmission, which in fact becomes perfect for a symmetric breather, is shown to be connected with localized eigenmodes thresholds. In the weak-coupling limit, the perfect reflection is shown to exist, which requires two scattering channels. A necessary condition for a system to have a perfect reflection is also considered in a general context.