  The discovery of the Higgs particle at 125 GeV has put strong constraints on
minimal messenger models of gauge mediation, pushing the stop masses into the
multi-TeV regime. Extensions of these models with matter-messenger mixing terms
have been proposed to generate a large trilinear parameter, $A_t$, relaxing
these constraints. The detailed survey of these models
\cite{Byakti:2013ti,Evans:2013kxa} so far considered messenger mixings with
only MSSM superfields. In the present work, we extend the survey to MSSM with
inverse-seesaw mechanism. The neutrino-sneutrino corrections to the Higgs mass
in the inverse seesaw model are not significant in the minimal gauge mediation
model, unless one considers messenger-matter interaction terms. We classify all
possible models with messenger-matter interactions and perform thorough
numerical analysis to find out the promising models. We found that out of the
17 possible models 9 of them can lead to Higgs mass within the observed value
without raising the sfermion masses significantly. The successful models have
stop masses $\sim $1.5 TeV with small or negligible mixing and yet a light CP
even Higgs at 125 GeV.
