Magnetostriction, parallel (lambda-parallel-to) and perpendicular (lambda-perpendicular-to) to the applied magnetic field, and thermal expansion measurements have been performed in a-Gd2Cu and a-(Gd90.98)Tb(0.02)2Cu. The volume (omega = lambda-parallel-to + 2-lambda-perpendicular-to) field-induced magnetostriction peaks at the magnetic transition temperatures. The anisotropic magnetostriction (lambda(t) = lambda-parallel-to - lambda-perpendicular-to) in a-Gd2Cu is non-null and also shows a peak; in the doped compound the peak no longer exists and lambda(t) increases down to low temperatures. The strain dependencies of the isotropic and longitudinal two-ion spin-exchange-correlation functions explain the results for a-Gd2Cu and the thermal dependence of omega in a-(Gd(0.98)Tb90.02)02Cu. The strong single-ion random anisotropy of Tb ions accounts for the lambda(t) behavior in the doped compound.