Divisibility conjecture for the generalized recurrence sequence $b_T$

Let $L=(1,-1)$ and $R=(1)$, and let $K$ be the parameter appearing in the definition of the generalized sequence $b_T$. Write $\operatorname{\underline{\deg}} K$ for its indicated degree. Divisibility conjecture for $b_T$. If $\operatorname{\underline{\deg}} K\geq 2$, then for every $h\in\mathbb{N}$ with $4\nmid h$, there exist infinitely many $n$ such that $l$ divides $b_T(n)$. The source presents this as a conjectural extension of Alkauskas's statement; the notation $l$ is not defined in the supplied context.