Gamow-Teller (GT) strength distributions have been investigated in a high-resolution (He-3,t) charge-exchange experiment on the double-beta (beta beta ) decaying nuclei Te-128 and Te-130. The experiment was carried out at the Research Center for Nuclear Physics, Osaka, with a 420-MeV incident He-3 beam and the Grand Raiden magnetic spectrometer. A final-state energy resolution of 35 keV was achieved. The extracted GT strength distributions at low excitation energies in the final nuclei I-128 and I-130 are presented and discussed in the context of the beta beta decay matrix elements for the two tellurium nuclei. The additional neutron pair in Te-130 seems to produce a moderate increase in the fragmentation of the low-energy GT distribution.