Look at the hem of my T-shirt above.
Is it natural to say "the hem of your T-shirt is folded up (not nice). Let/put it down" in everyday English?
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Straighten [out] fits well with things that naturally become crooked, crinkled, crenulated, or—as is the case here—folded. Unfold also works as a literal description.
Let down and put down sound more natural when the original arrangement is deliberate (e.g., to let down one's hair), which probably isn't the case with a T-shirt hem (except in sewing, where to let down or let out a hem is to remove the stitching).