The bad-part density limit conjecture for non-abelian groups of order $3p$

Let $p$ and $q$ be primes with $q<p$ and $q\mid p-1$, let $T_{p,q}$ denote the non-abelian group of order $pq$, and let $q_n$ be the $n$-th prime satisfying $3\mid q_n-1$. For a finite group $G$, let $\alpha(G)=\frac{|BP(G)|}{2^{\kappa(G)-1}-1}$, where $BP(G)$ is its set of bad parts. Define

$$\delta_n=\alpha(T_{q_n,3}).$$

Bad-part density limit conjecture for groups of order $3q_n$.

$$\lim_{n\rightarrow\infty}\delta_n=0.5.$$

The conjecture is based on the tabulated computations for groups $T_{p,3}$ and is presented after the authors observe that the preceding cyclic-and-dihedral conjecture does not hold for groups of order $3p$. No resolution is supplied in the given text.