  We experimentally investigate the dielectric response of the low-dimensional
gapped quantum magnet Cu$_2$Cl$_{4}\cdot$H$_8$C$_4$SO$_2$ near a magnetic
field-induced quantum critical point, which separates the quantum-disordered
and helimagnetic ground states. The observed magnetocapacitive effect
originates from an improper ferroelectric nature of the transition, which
itself is perhaps one of the best known realizations of Bose--Einstein
condensation of magnons. Despite that, we find that the magnetocapacitive
effect associated with the transition exhibits huge and very unusual
anharmonicities.
