  Schubert polynomials $\mathfrak{S}_w$ are polynomial representatives for
cohomology classes of Schubert varieties in a complete flag variety, while
Grothendieck polynomials $\mathfrak{G}_w$ are analogous representatives for the
$K$-theory classes of the structure sheaves of Schubert varieties. In the
special case that $\mathfrak{S}_w$ is a multiplicity-free sum of monomials, K.
M\'esz\'aros, L. Setiabrata, and A. St. Dizier conjectured that
$\mathfrak{G}_w$ can be easily computed from $\mathfrak{S}_w$ via M\"obius
inversion on a certain poset. We prove this conjecture.
