We study the recently measured β decay of 70Kr into 70Br within the framework of the large-scale shell model. The enhancement in the Gamow-Teller (GT) transition strength in Br70 compared to the β decay of the lighter Ge62 was suggested as an indication for increased neutron-proton (np) pairing correlation. To explore the np correlations in nuclei, we systematically examined the β-decay properties of the even-even nuclei A=58,62,66, and 70 into N=Z odd-odd nuclei. By employing an interaction involving solely J=1,T=0 and J=0,T=1 pairing matrix elements, we observe that the pairing does not necessarily lead to an enhancement in the GT strength for the same coupling strength. But with the inclusion of the g9/2 orbital, the GT strength can be increased with increasing np pairing in connection with the enhanced contribution from the g9/2 orbital. We further compare those results with realistic calculations in the fp and f5/2pg9/2 model space to gauge the contribution from f7/2 and g9/2 orbitals in the GT strengths. With the JUN45 interaction, there is an increment for the yrast 1+ state for the decay of Kr70 as compared to the decay of Ge62 due to increased g9/2 contribution. Additionally, we probe the effect of np pairing on BGT by modifying the single-particle energies and the T=0 matrix elements of the interaction responsible for the decay transition strength. In calculations with realistic interaction, we find that the accumulated transition strength can increase with enhanced np pairing.