I think that he half-Romulan orphan backstory was included in the novelization of TWOK to explain why Saavik was crying at Spock's funeral (at the director's insistance because of the emotional impact it has on the scene - think about it - if a Vulcan is crying, then the death of Spock is really sad).
No, the backstory was expanded by Vonda McIntyre, from the one line in the shooting script where Spock tells Kirk that Saavik's half Romulan, to make Vonda's novelization more interesting,
and to give some much-needed background to the characters of Peter Preston and Saavik, whom Vonda features heavily, in order to pad the story out to novel length. She certainly didn't do all that to explain away one tear in one scene of a movie that she didn't even see until after she turned in her manuscript. I just checked the script and the funeral scene says, of Saavik, only that she is watching attentively, along with Sulu, Uhura, Chekov and David, and that
"SAAVIK wears her hair down..."
No scripted mention of tears at all, so Vonda would have been oblivious to the director's choices.
The ShoWest presentation/long trailer is linked here: