  We study extreme-mass-ratio systems in theories admitting the Schwarzschild
solution and propagating a massive graviton. We show that, in addition to small
corrections to the quadrupolar and higher-order modes, a dipolar mode is
excited in these theories and we quantify its excitation. While
LIGO-Virgo-KAGRA observations are not expected to impose meaningful constraints
in the dipolar sector, future observations by the Einstein Telescope or by
LISA, together with bounds from dispersion relations, can rule out theories of
massive gravity admitting vacuum General Relativistic backgrounds. For the
bound to be circumvented, one needs to move away from Ricci-flat solutions, and
enter a territory where constraints based on wave propagation and dispersion
relations are not reliable.
