  We study the worldsheet scattering theory of the $\eta$ deformation of the
AdS$_\mathsf{5} \times $S$^\mathsf{5}$ superstring corresponding to the purely
fermionic Dynkin diagram. This theory is a Weyl-invariant integrable
deformation of the AdS$_\mathsf{5} \times $S$^\mathsf{5}$ superstring, with
trigonometric quantum-deformed symmetry. We compute the two-body worldsheet S
matrix of this string in the light-cone gauge at tree level to quadratic order
in fermions. The result factorizes into two elementary blocks, and solves the
classical Yang-Baxter equation. We also determine the corresponding exact
factorized S matrix, and show that its perturbative expansion matches our
tree-level results, once we correctly identify the deformed light-cone symmetry
algebra of the string. Finally, we briefly revisit the computation of the
corresponding S matrix for the $\eta$ deformation based on the distinguished
Dynkin diagram, finding a tree-level S matrix that factorizes and solves the
classical Yang-Baxter equation, in contrast to previous results.
