"There was a sequence scripted, but not filmed, explaining the reason for Saavik staying behind on Vulcan - she was pregnant from her Ponn Farr experience with Spock."
^This one is false........
They did film a scene where it is heavily implied that Saavik is pregnant. There are many stills of the scene floating around over the years.
It is right after McCoy's line "I just wish we could cloak the stench."
BONES
I just wish we could cloak the
stench.
And he starts off. WIDEN as Kirk turns to LT. SAAVIK
SAAVIK
Admiral, I'd like to continue my
work on the ship until you leave.
KIRK
Thank you, Lt. Saavik.
SAAVIK
(produces disc)
And... Here is a deposition I have
made. If it is not sufficient, I
will return to Earth to testify.
KIRK
Don't concern yourself, Saavik.
Your leave has been granted for good
and proper cause.
(a beat)
How are you feeling?
SAAVIK
I am well, Admiral.
KIRK
You will be in good hands here.
They exchange a look, and she starts in, leaving him
alone in thought. Then he slowly, almost secretly
looks upward: he stares uncertainly at the mountain
above.