The proportionality between differential cross sections at vanishing linear momentum transfer and Gamow-Teller transition strength, expressed in terms of the unit cross section (σGT), was studied as a function of target mass number for (t,He3) and (He3,t) reactions at 115A MeV and 140A MeV, respectively. Existing (He3,t) and (t,He3) data on targets with mass number 12≤A≤120 were complemented with new and reevaluated (t,He3) data on proton, deuteron, Li6, and C12 targets. It was found that in spite of the small difference in beam energies between the two probes, the unit cross sections have a nearly identical and simple dependence on target mass number A, for A≥12: σGT=109/A0.65. The factorization of the unit cross sections in terms of a kinematical factor, a distortion factor, and the strength of the effective spin-isospin transfer nucleus-nucleus interaction was investigated. Simple phenomenological functions depending on mass number A were extracted for the latter two. By comparison with plane and distorted-wave Born approximation calculations, it was found that the use of a short-range approximation for knock-on exchange contributions to the transition amplitude results in overestimated cross sections for reactions involving the composite (He3,t) and (t,He3) probes.