When Jemma left her arrival site, she left her necklace there to give a clue for Fitz. It was explicitly shown.

One month in, right before she meets Will, she says that she’s lost her way to the entry point. She has no necklace on.

Later on, when she’s in the cave with Will, just as she sewn up her leg, in the middle of the scene, her necklace appears (16:32 she doesn’t have it, 16:42 she has).

At around 24:00, when she and Will talk about Fitz and whether Will have somebody, she has it on. Next scenes, as she goes to bed and says good night to Fitz - no necklace.

When she breaks down and decides to go to the no-fly zone - no necklace.

Drawing on the map, realizing that the portal is moving, putting together the equipment - necklace on.

Talking about her scoliosis - the necklace appears in the middle of the scene. For the recalling part, she has no necklace, when she talks about the moons, she has the necklace.

New portal and message in the bottle - necklace on.

Around 36 mins in, when she and Will go up to see the sunrise, it is explicitly shown that she puts on the necklace.

What I couldn’t catch is whether she had it on when she was brought back to Earth.

Now, this easily could be a mistake. But then why show us two scenes when Jemma explicitly puts her necklace somewhere? What if it’s a clue? My theory: no necklace - reality (as it is left at the entry point); necklace on - hallucination/vision.