  In this paper, we investigate the contributions of anomalous quartic gauge
couplings (aQGCs) to $Z\gamma jj$ production at the Large Hadron Collider (LHC)
in the context of Standard Model effective theory (SMEFT). When energy scale is
large, the validity of SMEFT becomes an important issue. To ensure the
validity, the unitarity bound is applied in a model independent approach, which
is found to have significant suppressive effects on the signals of $O_{M_i}$
operators. The kinematic and polarization features of the aQGC signals are also
studied. The polarization effect is useful to highlight the signals of
$O_{T_i}$ operators. The sensitivity estimates on dimension-8 operators with
unitarity bounds at $\sqrt{s}=14$ TeV are obtained.
