  We have investigated the structural properties of strange quark stars (SQSs)
in a modified theory of gravity known as massive gravity. In order to obtain
the equation of state (EOS) of strange quark matter, we have employed a
modified version of the Nambu-Jona-Lasinio model (MNJL) which includes a
combination of NJL Lagrangian and its Fierz transformation by using weighting
factors ($1-\alpha $) and $\alpha$. Additionally, we have also calculated
dimensionless tidal deformability ($\Lambda$) in massive gravity. To constrain
the allowed values of the parameters appearing in massive gravity, we have
imposed the condition $\Lambda_{1.4 {M}_{\odot }}\lesssim580 $. Notably, in the
MNJL model, the value of $\alpha$ varies between zero and one. As $\alpha$
increases, the EOS becomes stiffer, and the value of $\Lambda$ increases
accordingy. We have demonstrated that by softening the EOS with increasing the
bag constant, one can obtain objects in massive gravity that not only satisfy
the constraint $\Lambda_{1.4 {M}% _{\odot }}\lesssim580$, but they also fall
within the unknown mass gap region ($2.5{M}_{\odot}-5{M}_{\odot }$). To
establish that the obtained objects in this region are not black holes, we have
calculated Schwarzschild radius, compactness, and $\Lambda_{{M_{TOV}}}$ in
massive gravity.
