Why did "The Girl" wipe her blood on Corso?

I think this was a decision on Polanski's part to suggest to the audience that perhaps "The Girl" is actually LCF - Lucifer, in particular, in the sense of "light bearer".

To me, the mark she makes looks like a trident - for example, what Death holds in his left hand in the fifth engraving:

...there are three verticle lines on Corso's forehead, one down his nose. Whatever it means, he's got her mark on his forehead for all the world to see.

Of note, this is not the mark as it is described in the book or the screenplay. On page 261 in chapter 12 "Buckingham and Milady" of Arturo Pérez-Reverte's "The Club Dumas" the mark she makes is described as four vertical lines:

She touched his face and drew four red lines with her fingers, from his forehead to his chin.

The mark she makes is described similarly in the screenplay:

69. PARIS HOTEL: BEDROOM INT/NIGHT

CORSO is filling a plastic laundry bag with ice from a tray in the minibar.

THE GIRL is sitting on the bed with her head tilted back and a bloodstained handkerchief to her nose. The bedside light bathes the room in a subdued glow.

...

Her nose has stopped bleeding.

THE GIRL: Do you believe in the Devil, Corso?

CORSO: I'm being paid to. Do you?

THE GIRL (smiles): I'm a bit of a devil myself...

She reaches up, removes his glasses, and puts them on the bedside table. CORSO eyes her uncertainly. Then the spell is broken: her nose starts to bleed again.

She puts her fingertips to it and inspects the blood on them. Very deliberately, she dabbles them in the blood some more, reaches up, and gently draws four vertical lines down his face from his forehead to his mouth, where her fingertips linger.

CORSO's face approaches hers. They melt into a passionate kiss, Then she pushes W= away, rolls him over on his back, unbuttons his shirt, and rests her palms on his chest. Playfully, she runs her forefinger over the imprint of Liana's teeth.

THE GIRL (smiles mischievously): Would you know a devil if you saw one?

In both the book and screenplay, the two get it on after she "marks him" but the movie takes a different course: Corso gets a call and goes down to the lobby to talk with Balkan on the phone. After that, with the blood still smeared on his face, he talks with the hotel clerk. At this point, I think Polanski is also just having a little fun with his good looking A-list actor - much the same way he relished cutting Nicholson's nose in "Chinatown." (Sorry, I don't have a reference, but I once saw an interview with him where he described the daring of a Director to mark up the lead actors face.)

...and Polanski does so in a way which works for Corso's character. He's not a man who is terribly concerned with his personal appearance, how he looks to other's or what they might think of him.

"The Girl" is still very mysterious at this point in the movie's story. We don't know what her motivation is, but she does keep protecting him. To what end, tho? For what purpose? Corso even asks her, "And you - where do you fit into it?" The phone rings and he answers it, so she does not have to answer. There is an obvious sexual tension between the two and Corso does seem to be coming under her spell. He even gets a little hypnotized by her changing iris color just prior to being marked - is he literally or actually under her spell? Is she just playing around? Is she practicing blood magic? We don't know, but there it is: her eye colors change and now he's got her blood on his face... in the shape of a trident.

As far as the movie is concerned, whether she is the devil, a guardian angel (she reply's "If you say so..." when Corso asks her on the plane ride if she is his), or "the whore of Babylon," I think Polanski is just making use of a powerful signifier to keep the dramatic tension heightened. There is a lot of religious significance to making a mark on the forehead (e.g. Ash Wednesday, Tilaka, etc.) as well as all the psychological significance of the "mask" one wears, how the world sees them, etc. Equally potent is the idea of "blood magic" and ritual body markings. Considering the "satanic" angle of the film, I think it is just a devilish little detail from the Director.

Similar to how Harry ("hairy"?) Angel realizes the pun of Louis Cypher's name as Lucifer, so too "LCF" refers to a name which can be read as "bringer of light." When Corso enters the Ninth Gate, is he becoming enlightened? Is he going to heaven? Or is the Ninth Gate perhaps a doorway out from the Kingdom of Shadows, i.e. the world as we know it is hell. Was this mark a part of her spell to help him stay on the path to the Ninth Gate? We can only speculate.

About the only analysis that I can even find on that portion is from this website, where it is compared to the Qabalah (or Kabbala) and the Tree of Life. I don't remember there being much of an explanation in the original book, "The Club Dumas".

Earlier, when Corso first expressed his admiration and gratitude to the girl for fighting for him against the albino down by the river, we saw the bond of Higher Feeling growing between them. It was at this point that the girl looked lovingly at Corso and drew with her fingers three vertical lines on his forehead with her own blood, the central line extending down his nose. There is a long spiritual tradition of marking the forehead as a sign of spiritual protection and initiation in both Eastern and Western traditions and three vertical marks on the forehead is the traditional Hindu sign of initiation of those who worship God in the form of Vishnu, the Preserver, whose qualities (like those of Chesed) are kindness and mercy. Such marks are also worn as a reminder of the consecration of the body as the temple of the Spirit, and in Corso's case might represent a sign of his initiation into Higher Feeling and the realm of the Soul. [Corso's blood stained forehead is not immediately cleaned.]

In the context of the Tree of Life, the three symbolic marks might also refer to the three Transcendent Creative energies of the Supernal Triad (which, when the body is superimposed on the Tree, are located in the head). The elongated center mark might symbolize the Central Pillar which extends downward from the highest central sephira of the Godhead, Kether/Crown, representing the route of the path of return which Corso is traveling. The girl begins as a symbolic figure who models for him the qualities of the Soul which he will gradually grow into, but once Corso has achieved the union of his ego and Soul, the inter-dimensional figure of the girl remains a symbol of the non-dual Spirit. It is his union with her in this capacity which will carry him across the Abyss and into union with the Spirit with the opening of the Ninth Gate.

The three finger mark looks like three hebrew letters vav (?) which symbolizes the number 6, meaning the mark would be 666 (like the Monster Energy drink logo). It could be the mark of the beast.

As to why 3, not 4 like in the movie, it would be interesting if like the story portrayed, one needed to compare three sources--the book, the screenplay, the movie--for esoteric meaning. The one that is different (in this case the movie) has the true meaning.

Also, because it's been noted above there's actually not as much as one might expect on the internet concerning all of the esoteric symbolism in the movie. So, I'm going to dump my observation here: he actually experiences all of the true "images" during the course of the movie. It's not head knowledge or a ritual for him. It is his lived experience.

This is because of a secret blood pact that takes place. It resembles the "I am you and you are me" in this movie.