Suppose $X_t$ is a Feller process and $q(x,\xi)$ is the symbol of $X$, which satisfies
$$
\lim_{t\downarrow 0} {\bf E}_x \frac{f(X_t)-f(X_0)}{t}=-(2\pi)^{-d/2} \int_{\mathbb{R}^d} e^{ix\cdot\xi}q(x,\xi)\hat{f}(\xi)\ d \xi, 
$$
for all $f\in C^\infty_c(\mathbb{R}^d)$. 

Assume 
$$
\sup_{x\in \mathbb{R}^d}|q(x, \xi)|\leq C(1+|\xi|), \quad\forall\xi\in \mathbb{R}^d
$$
and $\Gamma\subseteq \mathbb{R}^d$ with $\ dim(\Gamma)<d-1$. Is it possible to prove $\Gamma$ is a polar set, which means 
$$
{\bf P}_x(T_\Gamma<\infty)=0, \quad \forall x\in \mathbb{R}^d? 
$$
Here $T_{\Gamma}:=\inf\{t>0: X_t\in\Gamma \}$. 


Remark: If $X_t$ is a Levy process, I know how to prove this, but if $X_t$ is a general Felller process, I have no idea. One example of $q(x,\xi)$ is 
$$
q(x,\xi)= |\xi|^{\alpha}+i b(x)\cdot\xi. 
$$