  In this paper we are interested in the geometric local theta correspondence
at the Iwahori level for dual reductive pairs $(G,H)$ of type II over a
non-Archimedean field of characteristic $p\neq 2$ in the framework of the
geometric Langlands program. We consider the geometric version of the
$I_{H}\times I_{G}$-invariants of the Weil representation
$\mathcal{S}^{I_{H}\times I_{G}}$ as a bimodule under the of action
Iwahori-Hecke algebras $\mathcal{H}_{I_{G}}$ and $\mathcal{H}_{I_{H}}$ and we
give some partial geometric description of the corresponding category under the
action of Hecke functors. We also define geometric Jacquet functors for any
connected reductive group $G$ at the Iwahori level and we show that they
commute with the Hecke action of the $\mathcal{H}_{I_{L}}$-subelgebra of
$\mathcal{H}_{I_{G}}$ for a Levi subgroup $L$.
