  Gravitational wave `echoes' during black-hole merging events have been
advocated as possible signals of modifications to gravity in the strong-field
(but semiclassical) regime. In these proposals the observable effect comes
entirely from the appearance of nonzero reflection probability at the horizon,
which vanishes for a standard black hole. We show how to apply EFT reasoning to
these arguments, using and extending earlier work for localized systems that
relates choices of boundary condition to the action for the physics responsible
for these boundary conditions. EFT reasoning applied to this action argues that
linear `Robin' boundary conditions dominate at low energies, and we determine
the relationship between the corresponding effective coupling (whose value is
the one relevant low-energy prediction of particular modifications to General
Relativity for these systems) and the phenomenologically measurable
near-horizon reflection coefficient. Because this connection involves only
near-horizon physics it is comparatively simple to establish, and we do so for
perturbations in both the Schwarzschild geometry (which is the one most often
studied theoretically) and the Kerr geometry (which is the one of observational
interest for post-merger ring down). In passing we identify the
renormalization-group evolution of the effective couplings as a function of a
regularization distance from the horizon, that enforces how physics does not
depend on the precise position where the boundary conditions are imposed. We
show that the perfect-absorber/perfect-emitter boundary conditions of General
Relativity correspond to the only fixed points of this evolution. Nontrivial
running of all other RG evolution reflects how modifications to gravity
necessarily introduce new physics near the horizon.
