  In this paper, we study irreducible weight modules with infinite dimensional
weight spaces over the mirror-twisted Heisenberg-Virasoro algebra
$\mathcal{D}$. More precisely, the necessary and sufficient conditions for the
tensor products of irreducible highest weight modules and irreducible modules
of intermediates series over $\mathcal{D}$ to be irreducible are determined by
using "shifting technique". This leads to a family of new irreducible weight
modules over $\mathcal{D}$. Then we obtain that any two such tensor products
are isomorphic if and only if the corresponding highest weight modules and
modules of intermediate series are isomorphic respectively. Also we discuss
submodules of the tensor product module when it is not irreducible.
