  We revisit charged lepton flavor violating (CLFV) scattering processes
$\ell_{i} N \to \tau X \, (\ell_{i} \ni e, \mu)$ mediated by Higgs. We point
out that a new subprocess $\ell_{i} g \to \tau g$ via the effective
interactions of Higgs and gluon gives the dominant contribution to $\ell_{i} N
\to \tau X$ for an incident beam energy of $E_{\ell} \lesssim 1\,\text{TeV}$ in
fixed target experiments. Furthermore, in the light of quark number
conservation, we consider quark pair-production processes $\ell_{i} g \to \tau
q \bar{q}$ ($q$ denotes quarks) instead of $\ell_{i} q \to \tau q$. This
corrects the threshold energy of each subprocess contributing to
$\sigma(\ell_{i} N \to \tau X)$. Reevaluation of $\sigma(\ell_{i} N \to \tau
X)$ including all of relevant subprocesses shows that the search for $\ell_{i}
N \to \tau X$ could serve a complementary opportunity with other relevant
processes to shed light on the Higgs CLFV.
