Agreed, those regions with FA > 1 are overwhelming around the edge of the brain, and most likely due to background noise. You may chose to remove them using a more aggressive mask, but it’s by no means a requirements - it simply makes the images nicer to display.
Just to explain how you can get FA > 1: one way of defining FA is as the ratio of the variance in the eigenvalues of the tensor to their root-mean-square value, scaled such that the maximum physically possible FA value is 1. But what happens in noisy regions is that the b=0 and DW intensities are similar, so that the ratio of DWI to b=0 can be greater than 1, which leads to a negative ADC value. This is clearly non-physical, but nonetheless allowed by the fitting procedure. When this happens, it will lead to a greater variance than expected, and consequently an FA value greater than 1. While some fitting routines do constrain the eigenvalues to be positive, this requires expensive non-linear fitting routines, and we don’t see a huge benefit to using them since the problem is largely confined to non-brain regions anyway…