  We study the double Grothendieck polynomials of Kirillov--Naruse for the
symplectic and odd orthogonal Grassmannians. These functions are explicitly
written as sums of Pfaffian and are identified with the stable limits of the
fundamental classes of Schubert varieties in the torus equivariant connective
K-theory of these isotropic Grassmannians. We also provide a combinatorial
description of the ring formally spanned by double Grothendieck polynomials.
