  The direct detection of gravitational waves crowns decades of efforts in the
modelling of sources and of increasing detectors' sensitivity. With future
third-generation Earth-based detectors or space-based observatories,
gravitational-wave astronomy will be at its full bloom. Previously
brushed-aside questions on environmental or other systematic effects in the
generation and propagation of gravitational waves are now begging for a
systematic treatment. Here, we study how electromagnetic and gravitational
radiation is scattered by a binary system. Scattering cross-sections,
resonances and the effect of an impinging wave on a gravitational-bound binary
are worked out for the first time. The ratio between the scattered-wave
amplitude and the incident wave can be of order $10^{-5}$ for known pulsars,
bringing this into the realm of future gravitational-wave observatories. For
currently realistic distribution of compact-object binaries, the interaction
cross-section is too small to be of relevance.
