  Einstein-Maxwell dilaton-axion gravity is a string-inspired model arising
from the low energy effective action of heterotic string theory and an
important candidate as alternative to General Relativity. Recently, some
authors have explored its astrophysical implications in the spectra of
accreting black holes and inferred the constraint $r_2 < 0.1$, where $r_2 \ge
0$ is the black hole dilaton charge and General Relativity is recovered for
$r_2 = 0$. In the present paper, we study the impact of a non-vanishing black
hole dilaton charge on the reflection spectrum of the disk. From the analysis
of a NuSTAR spectrum of the black hole binary EXO 1846-031, we find the
constraint $r_2 < 0.011$ (90% CL), which is an order of magnitude more
stringent.
