The infinite-order polynomial bounded K-theory class conjecture

Let $G$ be the solvable group described in the source, with $BG$ homotopy equivalent to a closed oriented $3$-manifold, and let $E G$ be the homogeneous bar resolution. Let $\mathcal P$ denote the polynomial bounding class. Infinite-order polynomial bounded K-theory conjecture. The class $[C_\star(EG)]$ represents an element of infinite order in

$${\mathcal P}K^{\mathrm{rel}}_0(\mathbb{Z}[G]).$$

The group is given as an extension $\mathbb{Z}^2\to G\to\mathbb{Z}$ and is not $\mathcal B$-$\operatorname{\cal SIC}$ for any bounding class $\mathcal B\prec\mathcal E$. The conjecture would exhibit an explicit infinite-order obstruction in relative polynomial bounded $K$-theory; the source does not state that it has been resolved.