Background: The Gamow-Teller response of Ar40 is important for the use of liquid argon as a medium for neutrino detection. An ambiguity about the Gamow-Teller strength for the excitation of 1+ states at 2290 and 2730 keV in K40 results in a significant uncertainty for neutrino capture rates. This ambiguity is caused by the large discrepancy observed between strengths extracted from Ar40(p,n) charge-exchange data and the transition strengths for the analog transitions studied in the β decay of Ti40. Purpose: This study was aimed at resolving the ambiguity between the results from the Ar40(p,n) charge-exchange and Ti40 β-decay data. Method: Shell-model calculations in the sd-pf shell with a new interaction (WBMB-C) were used to study differences between the structure of the transitions from Ar40 and Ti40. Distorted-wave Born approximation reaction calculations were used to investigate uncertainties in the extraction of Gamow-Teller strength from the Ar40(p,n) data. New high-resolution data for the Ar40(He3,t) reaction were used to gain further insight into the charge-exchange reaction mechanism and to provide more information to test the validity of the shell-model calculations. Results: The shell-model calculations showed that interference between amplitudes associated with pf and sd components to the low-lying Gamow-Teller transitions, in combination with a difference in Coulomb energy shifts for Ar40 and Ti40, can produce the differences on the scale of those observed between the Ar40 charge-exchange and Ti40 β-decay data. In combination with the difference in nuclear penetrability of the (p,n) and (He3,t) probes, the different contributions from amplitudes associated with transitions in the pf and sd shells are likely also responsible for the observed discrepancy between the ratio of the cross sections for the low-lying 1+ states in the Ar40(p,n) and Ar40(He3,t) data. Conclusions: On the basis of this study, it is recommended to use Gamow-Teller strengths extracted from the Ar40(p,n) data, not the Ti40 β-decay data, for the calculation of neutrino capture rates. Further theoretical studies are required to achieve a consistent quantitative description for the energy differences between low-lying 1+ states in K40 and Sc40 and the experimentally observed Gamow-Teller strengths.