  We propose a new way to probe non-standard interactions (NSI) of neutrinos
with matter using the ultra-high energy (UHE) neutrino data at current and
future neutrino telescopes. We consider the Zee model of radiative neutrino
mass generation as a prototype, which allows two charged scalars -- one
$SU(2)_L$-doublet and one singlet, both being leptophilic, to be as light as
100 GeV, thereby inducing potentially observable NSI with electrons. We show
that these light charged Zee-scalars could give rise to a Glashow-like
resonance feature in the UHE neutrino event spectrum at the IceCube neutrino
observatory and its high-energy upgrade IceCube-Gen2, which can probe a sizable
fraction of the allowed NSI parameter space.
