  We investigate the worldsheet S matrix of string theory in $\eta$-deformed
$AdS_5\times S^5$. By computing the six-point tree-level S matrix we explicitly
show that there is no particle production at this level, as required by the
classical integrability of the theory. At one and two loops we show that
integrability requires that the classical two-particle states be redefined in a
non-local and $\eta$-dependent way. This is a significant departure from the
undeformed theory which is probably related to the quantum group symmetry of
the worldsheet theory. We use generalized unitarity to carry out the loop
calculations and identify a set of integrals that allow us to give a two-loop
Feynman integral representation of the logarithmic terms of the two-loop S
matrix. We finally also discuss aspects of the calculation of the two-loop
rational terms.
