Did Rusk know that the woman from the dating place was Blaney's ex wife?
Was he trying to set him up all along, or he just took advantage of the situation after the fact and murdered the girlfriend as a bonus?
Frenzy was a big comeback hit for Hitchcock in 1972, but there was always a creeping feeling that the script (by a noteable new playwright, Anthony Shaffer, from a "just OK" novel by Arthur LaBern) was a bit flimsy in parts, with gaps in logic or explanation.
..or maybe not.
Rusk's motivation for killing Brenda and Babs is in that category.
As a "base line," Frenzy suggests that Rusk is a serial killer of random women. "The Necktie Strangler" (some psychos love to showboat.) The first body we see (floating in the Thames) is "another necktie murder!" so there have been a few at that point. And we don't know the woman dead in bed at the end(in the book, THAT victim is Monica Barling, Brenda's secretary.)
But clearly, Rusk takes it upon himself to add "Richard Blaney's women" (ex wife Brenda and current girlfriend Babs) to his list of victims which is "making it personal" AND making things dangerous -- Blaney KNOWS Rusk, something might slip up and give Rusk away to Blaney.
And it does. When Blaney gives Rusk his bag of clothes to safeguard, Rusk puts the clothes, purse and ID of the dead Babs in the bag so that when the police open it...it looks like Blaney's the killer, but Blaney figures it out in seconds: "It's RUSK!") A great scene, I say. The clothes in the bag are "irrevocable proof" to the cops that Blaney is the killer, but they are also irrevocable proof to BLANEY that Rusk is the killer.
And Rusk knew that when he put the clothes in there.
So, Rusk's motivations become more clear:
Kill Blaney's women to frame Blaney
Watch Blaney run and hide and squirm as the wrong man -- on the streets of London, in the courtoom, in prison.
TELL Blaney -- "Hey, I'm the real killer" and watch nobody believe Blaney.
In short, this fits what we know of Rusk -- he's a sadist. He likes to sadistically toy with the women he rapes and kills(we see, just once, mercifully) and he sadistically toys with his "friend," Blaney.
CONT
CONT
But there is also this: once Rusk has "announced himself" (via the clothes) to Blaney as the killer, we start to realize:
Maybe, just maybe, Rusk wants to be caught.
We have read that real life psychos sometimes do. They'll write notes to the police like "Stop me before I kill again."
The cops and the judge don't believe Blaney about Rusk...Blaney is convicted and imprisoned..but Inspector Oxford follows the lead and figures out that Rusk is the real killer pretty quickly (which is ironic.)
On the whole, Rusk killing Blaney's women and turning Blaney into a wrong man allows Hitchcock to BLEND two of his thriller types: The Psycho Killer Story and The Wrong Man Story.
So that's another reason for Rusk's motivation.
Two side thoughts:
ONE: In RAPING and killing Blaney's two women, he gets to perversely "share" them with Blaney.
TWO: Interesting that he found his way to Brenda Blaney's "matchmaking service" and pretty much demonstrated to her IMMEDIATELY that he wanted women who liked being hurt. Rusk spends half his time hiding his crimes(the potato truck) and the other half giving himself away.)