  We study single top quark production in association with a lepton-neutrino
pair at the LHC within the framework of the Standard Model Effective Field
Theory (SMEFT). We focus on relevant two-quark-two-lepton operators
($O^{3}_{lq}$, $O^{1}_{lequ}$, and $O^{3}_{lequ}$). It is known that these
operators have tiny effects on the inclusive cross section of standard model tW
production and are thus typically ignored in the SMEFT searches. However, we
show that by employing smart observables, such as $m_{T2}$, the
pp$\rightarrow$t$\ell\nu$ process is significantly sensitive to these
operators. We set the most stringent limit on the coupling strength of the
$O^{3}_{lq}$ operator by reinterpreting the results of a search for new
phenomena with two opposite-charge leptons, jets and missing transverse
momentum at $\sqrt{s}$ = 13 TeV performed by the ATLAS collaboration. The
limits derived on the $O^{1}_{lequ}$ and $O^{3}_{lequ}$ operators are
comparable to those obtained from probing EFT effects in
pp$\rightarrow$t$\bar{\rm t}\ell\nu$ and pp$\rightarrow$t$\bar{\rm t}\ell\ell$
processes at the LHC. Consequently, we propose to include the effects of these
three operators on the pp$\rightarrow$t$\ell\nu$ process in future global SMEFT
analyses to increase the sensitivity and to reduce possible degeneracies.
