  Gravitational microlensing of gravitational waves (GWs) opens up the exciting
possibility of studying the spacetime geometry around the lens. In this work,
we investigate the prospects of constraining the `charged' hair of a black hole
(BH) from the observation of a GW signal microlensed by the BH. The charge can
have electromagnetic or modified gravity origin. We compute the analytic form
of the lensing potential with charge and construct the lensed waveforms for a
range of BH mass, charge and impact parameters, assuming non-spinning BHs.
Using an approximate likelihood function, we explore how future observations of
microlensed GWs can constrain the charge of the BH lens. We find that positive
values of the charge parameter (that can be of electromagnetic or modified
gravity origin) can be tightly constrained using lensed GW signals, while the
constraints on negative values of the charge parameter (modified gravity
origin) are modest.
