  In our previous work we investigated the effect of the hypothetical
reflecting boundary near the black hole event horizon on the waveform from
extreme mass-ratio inspirals (EMRIs). Even if the reflection efficiency is not
extremely high, we found that a significant modification of the waveform can be
expected. Then, the question is how to implement the search for this signature
in the actual data analysis of future space gravitational wave antennas, such
as LISA. In this paper we propose a simple but efficient method to detect the
signature of the reflecting boundary. The interesting feature of the effect of
the reflecting boundary on the orbital evolution of EMRIs is that the energy
and angular momentum loss rates periodically oscillate in the frequency domain.
The oscillation period is corresponding to the inverse time scale for the round
trip of gravitational waves between the hypothetical boundary and the angular
momentum barrier. We will show that this peculiar feature allows to detect the
signature of the reflecting boundary without much additional computational
cost.
