A note on smoothly slice links in $S^2\times S^2$

We give an alternative proof of a result of Miyazaki and Yasuhara that there exists links that are not smoothly slice in $S^2\times S^2$. We discuss potential applications to the detection of exotic $S^2\times S^2$. This is a follow-up note to a similar paper for the ${\mathbb{C}\mathbb{P}}^2\mathrm{\#}\overline{{\mathbb{C}\mathbb{P}}^2}$ case.