  Massive fields can exist in long-lived configurations around black holes. We
examine how the gravitational wave signal of a perturbed black hole is affected
by such `dirtiness' within linear theory. As a concrete example, we consider
the gravitational radiation emitted by the infall of a massive scalar field
into a Schwarzschild black hole. Whereas part of the scalar field is
absorbed/scattered by the black hole and triggers gravitational wave emission,
another part lingers in long-lived quasi-bound states. Solving numerically the
Teukolsky master equation for gravitational perturbations coupled to the
massive Klein-Gordon equation, we find a characteristic gravitational wave
signal, composed by a quasi-normal ringing followed by a late time tail. In
contrast to `clean' black holes, however, the late time tail contains small
amplitude wiggles with the frequency of the dominating quasi-bound state.
Additionally, an observer dependent beating pattern may also be seen. These
features were already observed in fully non-linear studies; our analysis shows
they are present at linear level, and, since it reduces to a 1+1 dimensional
numerical problem, allows for cleaner numerical data. Moreover, we discuss the
power law of the tail and that it only becomes universal sufficiently far away
from the `dirty' black hole. The wiggly tails, by constrast, are a generic
feature that may be used as a smoking gun for the presence of massive fields
around black holes, either as a linear cloud or as fully non-linear hair.
