This is the most contested question in the glutathione literature, and the honest summary is that it is unresolved rather than settled in either direction.
The case against oral availability is mechanistic and has direct human support. γ-Glutamyl transpeptidase is abundantly expressed on intestinal and hepatic surfaces, and it is the enzyme evolved to dismantle exactly this molecule. Anything crossing that barrier faces first-pass exposure to it. The 1992 study by Witschi and colleagues tested the prediction in humans with a large single oral load and found no meaningful rise in circulating glutathione, a result frequently cited as showing that oral glutathione is degraded to its constituent amino acids before reaching the systemic circulation.
The case for it comes from trials with different designs. The 2015 randomised controlled trial by Richie and colleagues supplemented over months and measured glutathione in blood compartments rather than tracking a single acute load, reporting increased body stores. These two results are not straightforwardly contradictory, because they measure different things: an acute plasma excursion and a chronic accumulation in stores are separable outcomes, and it is possible for the second to occur through salvaged constituent amino acids even if the intact tripeptide never survives absorption.
The comparative crossover work by Schmitt and colleagues probes that ambiguity from another angle by placing oral glutathione alongside N-acetylcysteine, which supplies cysteine to endogenous synthesis rather than delivering the tripeptide, and alongside a sublingual route that avoids first-pass metabolism. Studies of this kind are where the question will actually be settled, since they distinguish between 'glutathione cannot be absorbed' and 'glutathione status can be raised, but not by delivering intact glutathione to the gut'.
For present purposes the accurate statement is narrow: the intracellular biochemistry of glutathione is thoroughly characterised, whereas the effect of exogenous glutathione on human tissue glutathione status is a live disagreement in the primary literature with credible studies on both sides.