Here's the Obi-Wan and Luke scene as written in the script. I've italicized the deleted section, and bolded the part we're talking about.
BEN
The other he spoke of is your twin sister.
LUKE
But I have no sister.
BEN
Hmm. To protect you both from the Emperor, you were hidden from your
father when you were born. The Emperor knew, as I did, if Anakin were
to have any offspring, they would be a threat to him. That is the
reason why your sister remains safely anonymous.
LUKE
Leia! Leia's my sister.
BEN
Your insight serves you well. Bury your feelings deep down, Luke. They
do you credit.
But they could be made to serve the Emperor.
Luke looks into the distance, trying to comprehend all this.
BEN (continuing his narrative)
When your father left, he didn't know your mother was pregnant. Your
mother and I knew he would find out eventually, but we wanted to keep
you both as safe as possible, for as long as possible. So I took you
to live with my brother Owen on Tatooine... and your mother took Leia
to live as the daughter of Senator Organa, on Alderaan.
Luke turns, and settles near Ben to hear the tale.
BEN (attempting to give solace with his words)
The Organa household was high-born and politically quite powerful in
that system. Leia became a princess by virtue of lineage... no one knew
she'd been adopted, of course. But it was a title without real power,
since Alderaan had long been a democracy. Even so, the family
continued to be politically powerful, and Leia, following in her foster
father's path, became a senator as well. That's not all she became, of
course... she became the leader of her cell in the Alliance against the
corrupt Empire. And because she had diplomatic immunity, she was a
vital link for getting information to the Rebel cause. That's what she
was doing when her path crossed yours... for her foster parents had
always told her to contact me on Tatooine, if her troubles became
desperate.
Luke is overwhelmed by the truth, and is suddenly protective of his
sister.
LUKE
But you can't let her get involved now, Ben. Vader will destroy her.
BEN
She hasn't been trained in the ways of the Jedi the way you have,
Luke... but the Force is strong with her, as it is with all of your
family. There is no avoiding the battle. You must face and destroy
Vader!