Reionization is an inhomogeneous process, thought to begin in small ionized bubbles of the intergalactic medium (IGM) around overdense regions of galaxies. Recent Lyman-alpha (Lyα) studies during the epoch of reionization show growing evidence that ionized bubbles formed earlier around brighter galaxies, suggesting higher IGM transmission of Lyα from these galaxies. We investigate this problem using IR slitless spectroscopy from the Hubble Space Telescope (HST) Wide-Field Camera 3 (WFC3) G102 grism observations of 148 galaxies selected via photometric redshifts at 6.0 < z < 8.2. These galaxies have spectra extracted from the CANDELS Lyα Emission at Reionization (CLEAR) survey. We combine the CLEAR data for 275 galaxies with the Keck/DEIMOS+MOSFIRE dataset from the Texas Spectroscopic Search for Lyα Emission at the End of Reionization Survey. We then constrain the Lyα equivalent-width (EW) distribution at 6.0 < z < 8.2, which is described by an exponential form, dN/dEW ∝ exp(-EW)/W 0 , with the characteristic e-folding scale width (W 0 ). We confirm a significant drop of the Lyα strength (or W 0 ) at z > 6. Furthermore, we compare the redshift evolution of W 0 between galaxies at different UV luminosities. The UV-bright (M UV < −21, or L UV > L * ) galaxies show weaker evolution with a decrease of 0.4 (±0.2) dex in W 0 at z > 6 while UV-faint (M UV > −21, or L UV < L * ) galaxies exhibit a significant drop by a factor of 0.7-0.8 (±0.2) dex in W 0 from z < 6 to z > 6. Our results add to the accumulating evidence that UV-bright galaxies exhibit boosted Lyα transmission in the IGM, suggesting that reionization completes sooner in regions proximate to galaxies of higher UV luminosity.