  We provide identities of inverse Chevalley type for the graded characters of
level-zero Demazure submodules of extremal weight modules over a quantum affine
algebra of type $C$. These identities express the product $e^{\mu} \,
\mathrm{gch} \, V_{x}^{-}(\lambda)$ of the (one-dimensional) character
$e^{\mu}$, where $\mu$ is a (not necessarily dominant) minuscule weight, with
the graded character $\mathrm{gch} \, V_{x}^{-}(\lambda)$ of the level-zero
Demazure submodule $V_{x}^{-}(\lambda)$ over the quantum affine algebra
$U_{\mathsf{q}}(\mathfrak{g}_{\mathrm{af}})$ as an explicit finite linear
combination of the graded characters of level-zero Demazure submodules. These
identities immediately imply the corresponding inverse Chevalley formulas in
the torus-equivariant $K$-group of the semi-infinite flag manifold
$\mathbf{Q}_{G}$ associated to a connected, simply-connected and simple
algebraic group $G$ of type $C$. Also, we derive cancellation-free identities
from the identities above of inverse Chevalley type in the case that $\mu$ is a
standard basis element $\varepsilon_{k}$ in the weight lattice $P$ of $G$.
