  We compute the leading finite-size effects on the normalized structure
constants in semiclassical three-point correlation functions of two finite-size
giant magnon string states and three different types of "light" states -
primary scalar operators, dilaton operator with nonzero momentum and singlet
scalar operators on higher string levels. This is done for the case of
TsT-transformed, or gamma-deformed, AdS_5 x S^5 string theory background, dual
to N = 1 super Yang-Mills theory in four dimensions, arising as an exactly
marginal deformation of N = 4 super Yang-Mills.
