  Recently, it has been proposed that the black hole greybody factors can be
important to model ringdown spectral amplitudes. We study the stability of
greybody factors against a small-bump correction in the perturbation equation.
We find (I) that the greybody factor is stable in the frequency region relevant
to ringdown and (II) that it is destabilized at higher frequencies, especially
for a sharper bump correction. This behavior is similar to the case of higher
overtones, which is also very sensitive to a small correction. We clarify this
(in)stability with the WKB analysis. As the greybody factor is stable at the
frequency region relevant to the main part of ringdown, we conclude that the
greybody factor is suitable to model ringdown amplitude. In order to
investigate a bump correction in a self-consistent manner, we consider the
small-bump correction that can be realized in the general framework of
effective field theory of black hole perturbations.
