We construct string topology operations in twisted K-theory. We study the examples given by symplectic Grassmannians, computing Kz.ast;τ(LHPℓ) CMMI6.-1.lscript) in detail. Via the work of Freed-Hopkins- Teleman, these computations are related to completions of the Verlinde algebras of Sp(n). We compute these completions, and other relevant information about the Verlinde algebras. We also identify the completions with the twisted K-theory of the Gruher-Salvatore pro-spectra. Further comments on the field-theoretic nature of these constructions are made.