We consider giant magnons propagating in a γ-deformed AdS₅ × S⁵ background obtained from AdS₅ × S⁵ 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 (2|2) ⊕ (2|2)-invariant world-sheet S-matrix and the dressing factor. The γ-dependence in the limit is only due to different level-matching conditions. We consider the reduction of the deformed model to R × S³ and determine the leading γ-dependence of the dispersion relation for a finite J giant magnon.