  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.
