  Given a Schubert class on $Gr(k,V)$ where $V$ is a symplectic vector space of
dimension $2n$, we consider its restriction to the symplectic Grassmannian
$SpGr(k,V)$ of isotropic subspaces. Pragacz gave tableau formulae for
positively computing the expansion of these $H^*(Gr(k,V))$ classes into
Schubert classes of the target when $k=n$, which corresponds to expanding Schur
polynomials into $Q$-Schur polynomials. Coskun described an algorithm for their
expansion when $k\leq n$. We give a puzzle-based formula for these expansions,
while extending them to equivariant cohomology. We make use of a new
observation that usual Grassmannian puzzle pieces are already enough to do some
$2$-step Schubert calculus, and apply techniques from quantum integrable
systems (``scattering diagrams'').
