  We consider the Etingof-Kazhdan quantum vertex algebra
$\mathcal{V}^c(\mathfrak{gl}_N)$ associated with the trigonometric $R$-matrix
of type $A$. By combining Li's theory of $\phi$-coordinated modules and the
ideas from our previous paper, we introduce the notion of deformed
$\phi$-coordinated quantum vertex algebra module. We show that the orthogonal
twisted $h$-Yangians and restricted modules for the generalized orthogonal
twisted $h$-Yangians can be equipped with the structure of (truncated) deformed
$\phi$-coordinated $\mathcal{V}^c(\mathfrak{gl}_N)$-module and demonstrate its
applications.
