  The gauge invariant two-photon exchange (TPE) contributions in $e^-\pi^+
\rightarrow e^-\pi^+$ are discussed at hadronic level. The contact term is
added to keep the full amplitude gauge invariant by two methods: one is to
multiply form factors with the point-like particles scattering amplitude and
another is to construct a gauge invariant Lagangian. The practical calculations
show the TPE corrections by these two methods are almost the same, while the
later method is favored when extending the discussion to processes including
two charged finite-size particles like $ep \rightarrow en\pi^+$.
