  Let $\mathcal G$ be a stratified Lie group and $\{\X_j\}_{1 \leq j \leq n}$ a
basis for the left-invariant vector fields of degree one on $\mathcal G$. Let
$\Delta = \sum_{j = 1}^n \X_j^2 $ be the sub-Laplacian on $\mathcal G$. The
$j^{\mathrm{th}}$ Riesz transform on $\mathcal G$ is defined by $R_j:= \X_j
(-\Delta)^{-\frac{1}{2}}$, $1 \leq j \leq n$. In this paper, we provide a
concrete construction of the "twisted truncated sector" which is related to the
pointwise lower bound of the kernel of $R_j$ on $\mathcal G$. Then we obtain
the characterisation of compactness of the commutators of $R_j$ with a function
$b\in$ VMO$(\mathcal G)$, the space of functions with vanishing mean
oscillation on $\mathcal G$.
