  We show that various flavors of Witt vectors are functorial with respect to
multiplicative polynomial laws of finite degree. We then deduce that the
$p$-typical Witt vectors are functorial in multiplicative polynomial maps of
degree at most $p-1$. This extra functoriality allows us to extend the
$p$-typical Witt vectors functor from commutative rings to
$\mathbb{Z}/2$-Tambara functors, for odd primes $p$. We use these Witt vectors
for Tambara functors to describe the components of the dihedral fixed-points of
the real topological Hochschild homology spectrum at odd primes.
