This is not because the Third Sister knows that Leia is Anakin Skywalker's child; it is because the Third Sister found a link between Obi-Wan and Bail Organa and she believed Obi-Wan would do anything to save Bail's daughter.
Does the Third Sister Know about Luke Skywalker? Apparently, she does. During the episode, Kenobi received a message from Bail Prestor Organa asking about the whereabouts of the Jedi Master and mentioning Luke's location. During the clashes with the Empire, Kenobi lost the transmitter, which Reva promptly retrieved.
She has uncovered a connection between Leia's father, BAIL ORGANA, and Obi-wan Kenobi. She kidnaps Leia hoping that it will force Bail to go to Obi-wan for help, which he does. She didn't know Leia was related to Vader or Padmé, just to a friend of Obi-wan's: Bail.
In the show, young Leia was kidnapped in a secret attempt to flush the Jedi Master out of hiding after Reva learned about his special connection with Bail Organa (Jimmy Smits).
However, Leia's strong-mindedness during Vader's probe denied him the opportunity to discover she was his daughter. That serves to justify Vader's lack of awareness of his connection to Leia, although, perhaps, not as satisfyingly as if Lucas had planned for the relationship from the beginning.
However, she chose not to tell Anakin, presumably because he was about to go into a battle. Anakin was prone to letting his emotions affect him, and knowing that Padme was pregnant would've thrown him completely off the task. And Padme probably didn't think that her husband would be fighting battles for months to come.
Even though he had a fierce confrontation with Leia Organa during the opening scenes of 'Star Wars Episode IV: A New Hope,' he never even suspected she was his daughter. That was why the only person Vader targeted and tried to convince to turn to the dark side was Luke, as he didn't even know that he had a sister.
The Third Sister was at the Jedi Temple during Order 66. She either saw Anakin kill her fellow Jedi or saw the recording of his crimes. That's why she has such hatred for Obi-Wan. She was a Padawan who escaped Order 66.
Seething with ambition, Reva hunts down Jedi survivors of Order 66 as an Inquisitor. She wears the sleek armor of the secret order, and brandishes a unique lightsaber that can split in two to maximize her lethality.
It's well known that Star Wars lead characters Luke Skywalker and Princess (now General) Leia are brother and sister. The estranged siblings didn't know about their familial relationship until "Return of the Jedi." They even shared a passionate kiss in the previous movie, "The Empire Strikes Back."
Her droid picks up Obi-Wan, Vader gives up and walks away. Meanwhile, Reva manages to find the hidden passageway Leia used earlier in the episode. Through the power of editing and teleportation, she manages to make it through the passageway ahead of Leia…
The Inverse analysis — The new revelation that Leia was buddies with Obi-Wan when she was a kid isn't just some cool canon twist, it also adds a tragic layer to everything that happens in A New Hope.
Theory 1: Leia Doesn't Remember Ben Is Obi-Wan
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan.
Following the Wampa attack during the movie's opening scenes on Hoth; Leia, Han, and Chewie visit Luke in the infirmary. Leia is annoyed with Han, who insists she has feelings for him, so she kisses Luke to prove she doesn't. Presumably, the scene was simply meant to make Han jealous.
Reva knows that Anakin Skywalker is Darth Vader because she was one of his targets—a child—during the Order 66 killings that took place during the events of Star Wars Episode III: Revenge of the Sith.
Leia was facing away from Padmé when she was born as she was being held by a midwife droid. Meanwhile, Luke was in a similar position as he was being held by Obi-Wan. The reason Leia likely remembers Padmé is that she could sense her mother's emotions at the time of the senator's passing.
As the Third Sister, she was highly ambitious. Thus, her mind was set on tracking down Jedi Master Obi-Wan Kenobi, with her fellow Inquisitors assuming she hoped his capture would gain her Darth Vader's favor and therefore improve her station.
In the Star Wars film franchise, Obi-Wan does not have a known brother. However, he almost did. In the original Star Wars: Episode VI – Return of the Jedi screenplay, Obi-Wan did have a brother, and it was none other than Owen Lars (Joel Edgerton)—Luke Skywalker's step-uncle and Anakin's step-brother.
You'll be surprised to hear that in the original screenplay for "Star Wars: Episode VI - Return of the Jedi," Obi-Wan does have a brother, and it's none other than Luke Skywalker's uncle, Owen Lars. This detail never made it to the film's final cut, but it was still included in the movie's novelization.
Reva Sevander, better known as the Third Sister, is the secondary antagonist of the 2022 Disney+ Star Wars miniseries Obi-Wan Kenobi. She was a Jedi youngling who survived Order 66 and fell to the dark side of the Force, joining the Galactic Empire by becoming part of the Inquisitorius.
Although Reva became consumed by grief and then anger, her turn to the dark side was motivated by a desire to destroy Darth Vader, not by a desire to serve him. This leaves Reva as an excellently complicated villain on Obi-Wan Kenobi.
Reva was herself skewered by Anakin's lightsaber. But the blow was not lethal—it is said that she drew upon the dark side to keep herself from dying. She also successfully feigned death to avoid further brutality. This enabled Reva to survive the Great Jedi Purge, but the course of her life had unalterably changed.
In Bloodlines, Leia stated that she does not forgive Vader, and isn't convinced of his redemption. Surely, she spoke to Luke about how he was able to pull Anakin back to the light. Luke was able to connect with his father before he died, and forgive him for all the bad things he had done. But Leia can't.
Darth Vader found out that Luke was his son through Boba Fett, who revealed to him that the name of the Rebel that destroyed the Death Star was Luke Skywalker. That was when Darth Vader put the pieces together and discovered that this boy, unusually strong in the Force, was actually his son.