Giant magnons in TsT-transformed AdS_5 x S^5

We consider giant magnons propagating in a \gamma-deformed AdS_5 x S^5 background obtained from AdS_5 x S^5 by means of a chain of TsT transformations. We point out that in the light-cone gauge and in the infinite J limit the deformed and undeformed string models share the same magnon dispersion relation, the \su(2|2)\oplus \su(2|2)-invariant world-sheet S-matrix and the dressing factor. The \gamma-dependence in the limit is only due to different level-matching conditions. We consider the reduction of the deformed model to R x S^3 and determine the leading \gamma-dependence of the dispersion relation for a finite J giant magnon.