Fiber Bragg grating (FBG) inscription in standard fibers with femtosecond (fs) laser pulses was first reported nearly two decades ago. FBG fs inscription through the fiber polymer coating was recently demonstrated with a phase mask (PM) and High Numerical Aperture (High-NA) cylindrical lenses. In this work, we report on a new technique for FBG inscription through the acrylate polymer coating of optical fibers using a Low-NA lens and the PM. The FBGs were inscribed through the polymer coating of the fiber after a suitable fs photo-treatment process that was done to the polymer coating. We experimentally demonstrate inscription of high-quality FBGs yet with some damage to the coating. We characterize the wavelength sensitivity to strain and temperature of the inscribed FBGs, and compare them to FBGs that were inscribed in fibers that have undergone stripping, inscription, and recoating. The technique may simplify FBGs inscription through the coating especially in large mode area fibers and double clad fibers for laser applications in the future.