= Solution
On shell, the contact vertex is $4i\lambda^2m^2$. At a cubic vertex with two external on-shell legs and internal momentum $k$, the rule reduces to $2i\lambda(k^2-m^2)$. The propagator cancels one such factor, so the three exchange diagrams sum to
$$
-4i\lambda^2[(s-m^2)+(t-m^2)+(u-m^2)].
$$
For equal-mass two-to-two scattering, $s+t+u=4m^2$, and the exchange sum is $-4i\lambda^2m^2$. It cancels the contact diagram exactly. Thus the connected on-shell amplitude vanishes, as required by the <equivalence theorem for field redefinitions>: an invertible local field redefinition cannot turn a free theory into a physically interacting one.
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