Several recent cosmological analyses have found tension between constraints derived from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) data and those derived from other data sets, such as the Planck cosmic microwave background (CMB) temperature anisotropies. Similarly, a direct cross-correlation of the CFHTLenS data with Planck CMB lensing data yielded an anomalously low amplitude compared to expectations based on Planck or WMAP-derived cosmological parameters Liu and Hill. One potential explanation for these results is a multiplicative bias afflicting the CFHTLenS galaxy shape measurements, from which shears are inferred. Simulations are used in the CFHTLenS pipeline to calibrate such biases, but no data-driven constraints have been presented to date. A value of m ~ 0.9 would suffice to reconcile the amplitude of density fluctuations inferred from the CFHTLenS shear two-point statistics with that inferred from Planck CMB temperature data. This scenario is consistent with our results.