  Symmetric Grothendieck polynomials are inhomogeneous versions of Schur
polynomials that arise in combinatorial $K$-theory. A polynomial has saturated
Newton polytope (SNP) if every lattice point in the polytope is an exponent
vector. We show Newton polytopes of these Grothendieck polynomials and their
homogeneous components have SNP. Moreover, the Newton polytope of each
homogeneous component is a permutahedron. This addresses recent conjectures of
C. Monical-N. Tokcan-A. Yong and of A. Fink-K. M\'esz\'aros-A. St. Dizier in
this special case.
