We demonstrate an increase of optical transmittance and saturable absorption of laser-treated free-standing single-walled carbon nanotube (SWNT) films. The combined acid and low-power non-destructive laser treatment ensures an enhancement of linear transmittance across the visible range and double-digit increase of the saturable absorption of femtosecond laser radiation at 795 nm. The saturable absorption coefficient and the ratio of saturable to non-saturable losses increase by 26% and 35%, correspondingly, while the saturation intensity decreases by 20% because of the treatment. Our analysis indicates that with the performed treatment one can significantly improve the nonlinear optical properties of free-standing SWNT-based ultrafast saturable absorbers.