A Ga-71(He-3,t)Ge-71 charge-exchange experiment was performed to extract with high precision the Gamow-Teller (GT) transition strengths to the three lowest-lying states in Ge-71, i.e., the ground state (1/2(-)), the 175 keV (5/2(-)) and the 500 key (3/2(-)) excited states. These are the relevant states, which are populated via a charged-current reaction induced by neutrinos from reactor-produced Cr-51 and Ar-37 sources. A precise measurement of the GT transition strengths is an important input into the calibration of the SAGE and GALLEX solar neutrino detectors and addresses a long-standing discrepancy between the measured and evaluated capture rates from the Cr-51 and Ar-37 neutrino calibration sources, which has recently spawned new ideas about unconventional neutrino properties.