  Recently, Guo and Sun derived an identity for factorial Grothendieck
polynomials which is a generalization of the one for Schur polynomials by
Feh\'er, N\'emethi and Rim\'anyi. We analyze the identity from the point of
view of quantum integrability, based on the correspondence between the
wavefunctions of a five-vertex model and the Grothendieck polynomials. We give
another proof using the quantum inverse scattering method. We also apply the
same idea and technique to derive an identity for factorial Grothendieck
polynomials for rectangular Young diagrams. Combining with the Guo-Sun
identity, we get a duality formula. We also discuss a $q$-deformation of the
Guo-Sun identity.
