  We discuss the Grassmann graph $J_q(N,D)$ with $N \geq 2D$, having as
vertices the $D$-dimensional subspaces of an $N$-dimensional vector space over
the finite field $\mathbb{F}_q$. This graph is distance-regular with diameter
$D$; to avoid trivialities we assume $D\geq 3$. Fix a pair of a Delsarte clique
$C$ of $J_q(N,D)$ and a vertex $x$ in $C$. We construct a $2D$-dimensional
irreducible module $\mathbf{W}$ for the Terwilliger algebra $\mathbf{T}$ of
$J_q(N,D)$ associated with the pair $x$, $C$. We show that $\mathbf{W}$ is an
irreducible module for the confluent Cherednik algebra $\mathcal{H}_\mathrm{V}$
and describe how the $\mathbf{T}$-action on $\mathbf{W}$ is related to the
$\mathcal{H}_\mathrm{V}$-action on $\mathbf{W}$. Using the
$\mathcal{H}_\mathrm{V}$-module $\mathbf{W}$, we define non-symmetric dual
$q$-Hahn polynomials and prove their recurrence and orthogonality relations
from a combinatorial viewpoint.
