  The use of the SMEFT Lagrangian to quantify possible Beyond the Standard
Model (BSM) effects is standard in LHC and future collider studies. One of the
usual assumptions is to truncate the expansion with the dimension-$6$
operators. The numerical impact of the next terms in the series, the
dimension-$8$ operators, is unknown in general. We consider a specific BSM
model containing a charge-${2 3}$ heavy vector-like quark and compute the
operators generated at dimension-$8$. The numerical effects of these operators
are studied for the $t\bar{t}h$ process, where they contribute at tree level
and we find effects at the ${\cal{O}}(0.5-2\%)$ level for allowed values of the
parameters.
