  Let $X$ be an integral affine or projective hypersurface over a field $F$ of
characteristic $p>0$, and let $F(X)$ denote its function field. In a recent
article, Dolphin and Hoffmann obtained an explicit description of the kernel of
the natural restriction homomorphism between the rings of absolute K\"{a}hler
differentials of $F$ and $F(X)$, respectively. In this note, we examine the
possibility of deriving an analogous result for mod-$p$ Milnor $K$-theory using
the Bloch-Gabber-Kato theorem.
