  The past 10 years have seen remarkable progress in our capability of
analyzing reflection features in the X-ray spectra of accreting black holes.
Today X-ray reflection spectroscopy is a mature technique and a powerful tool
for studying the accretion process around black holes, measuring black hole
spins, and testing Einstein's theory of General Relativity in the strong field
regime. However, current reflection models still rely on a number of
simplifications and caution is necessary when we derive very precise
measurements. In this paper, we study the impact of the returning radiation on
our capability of measuring the properties of black holes using X-ray
reflection spectroscopy, and in particular on our capability of testing the
Kerr black hole hypothesis. While the returning radiation alters the reflection
spectrum of the disk, from the analysis of our simulations we find that models
without returning radiation can normally recover well the correct black hole
spin parameters and can test the Kerr metric. Our study thus confirms that
current tests of the Kerr hypothesis using X-ray reflection spectroscopy can be
robust.
