I think the items that were taken, and that weren't taken is telling.
A zebra striped pillow case was taken. IIRC there were two identical pillows. Only one pillow case was taken, and the pillow itself was left behind. The profiler suggest that this may be a "souvenir" that the perp has taken. But there may be even more to it. It was taken in such an obvious way. Everyone who walks into that room will immediately see that the pillow case is missing. It is like the perp really wanted LE to notice that (s)he had taken the pillow case.
The perp may also have taken the underwear. This could be also a "souvenir". But the murderer could also have known that serial rapist/murderers often take such items, and that the motive was not sexual perversion but something else entirely.
If JT was the murderer, like LE seems to think, that it would be strange for him to take "souvenirs",
because Julia's belongings would go to the Turnquist family anyway. Taken souvenirs would be an unnecessary risk.
The key might just have been taken for practical reasons, namely to lock the bedroom door on the way out. But as some have suggested, the murderer also may have wanted to come back.
Regarding the gloves, I am wondering how the blood got on it. From the description of the crime scene there was only a wound in the tongue. Could the gloves have been used to gag?