Non-triviality conjecture for generalized alternating knots

Let $F$ be a closed surface embedded in $S^3$, and let $K$ be a knot contained in $F\times[-1,1]$ with a reduced, prime, alternating diagram on $F$.

Non-triviality conjecture. $K$ is not trivial for $F$.

This conjecture concerns whether generalized alternating knots on closed surfaces can be trivial for the surface. The source provides no resolution status for the claim.