  We study how Rankin-Selberg periods interact with integral structures in
spherical Whittaker type representations. Using this representation-theoretic
framework, we show that the local Euler factors appearing in the construction
of the motivic Rankin-Selberg Euler system for a product of modular forms are
integrally optimal; i.e. any construction of this type with any choice of
integral input data would give local factors appearing in tame norm relations
at $p$ which are integrally divisible by the Euler factor
$\mathcal{P}_p^{'}(\mathrm{Frob}_p^{-1})$ modulo $p-1$.
