A dark mark left after a spot heals can look much more noticeable under a bright bathroom light. It is understandable to wonder whether glutathione could lighten the mark or make the whole face paler. Those goals are different.
Treating uneven pigmentation means addressing excess colour in selected areas, while changing your natural complexion is a broader and less predictable expectation.
Glutathione has been studied in connection with skin pigmentation, but results are not consistent enough to promise a particular shade, a fixed treatment period, or a permanent change. The safest discussion starts with identifying the actual skin concern rather than assuming every dark patch needs whitening.