This paywalled article does suggest that glutamine dosage does reduce DOMS to a degree and that mobility returned after 36 hours (though the abstract didn't really report the return of mobility for the placebo group).
Glutamine is a nonessential amino acid, meaning that our body produces it, which makes sense because it is used for a lot of functions aside from building muscle. (Like it's a nitrogen donor for anabolic processes, carbon donor for keeping the citric acid cycle going, regulates pH in our kidneys, and transports ammonia through our body, among others)
While replenishing some glutamine may help in the post-workout, you might as well just do a regular protein shake instead of just focusing on glutamine. It seems silly to take a nonessential amino acid when our body makes it and it'd be better to take something that replenishes essential amino acids since our bodies don't make those.