Pilar starts to swap out her +6 Splendour headband for +4 Intelligence -

Pilar doesn't need an Intelligence headband either.  Pilar is pretty smart on her own.  Pilar has mostly been using her Intelligence headband as an excuse to actually think about things, not to solve problems that were too hard for Pilar without it.

Pilar has lived through a lot of evidence at this point.  How does her specialability work?

...well, if Pilar didn't Gate into Dispater's throne room from Cheliax - which Pilar obviously didn't, because you can't reach Dis except from Avernus - then, Pilar must have followed along with the Most High and Carissa Sevar without being aware of it.  But Dispater noticed, because Dispater said afterwards that He was wondering if Snack Service was going to interfere and if Snack Service thought it could evade His notice.

Pilar's ability has never felt like Teleportation to her.  That she was walking places in an ordinary way, but nobody was noticing, was the main theory Pilar had in the back of her mind.  So far as Pilar knows, everything she's done could have been done by sneaking around without anybody noticing including herself.

Except for Tonia, who suddenly found herself outside of Project Lawful's Forbiddance while Pilar was inside a torture room.

How would that work?  Tonia sneaking outside and other people not remembering her?

Are sneaking, concealment, secrecy, or memory usually considered parts of Cayden Cailean's domain?

...no?

So what part of Cayden Cailean's domain is Pilar wielding?  Pilar's dislike of thinking about Cayden Cailean is preventing Pilar from thinking about her own abilities, to the point where it's inhibiting Pilar's ability to serve Asmodeus.

...Snack Service called Cayden Cailean the glorious and exalted god of parties, sex, and drunken blackouts at one point, didn't it.

Does Pilar actually just have a drunken blackout so hard that other people can't remember her either?

Nnnoooot exactly, but close enough.

It's more like an Invisibility or a Sanctuary spell, where you can't be seen, or can't be attacked, in exchange for not being able to attack or cast targeted spells yourself.

Pilar promises not to remember herself, nor attack anyone or target spells, nor steal anything, nor... do anything imbalanced, one might say, though that part has to do with ancient godagreements and not just the structure of magic.  In exchange, other people don't remember Pilar either, and she doesn't set off alarm spells.

And I cursed Tonia to walk out of our Forbiddance in an unmemorable drunken blackout of her own?  That seems - too powerful, imbalanced like you put it.  If I can just make other people do things like that, later, without my even being there...

...I escorted Tonia out of the Forbiddance myself, didn't remember it, and left Tonia there in a drunken blackout until it was time for her to wake up later.

Thaaaaat's right!

How did I sneak up on the spy trying to Helm of Brilliance the Queen's celebration, if I can't attack anyone using my specialability?

Pilar didn't black out during that.  That's why you remember sneaking!  Pilar just changed into a nicer dress that made her fit in at the party, entered into the ballroom like she'd always been at that party, walked around like she was just part of the party, and surprised the spy with a trip to a nice afterlife.

...people could see me the whole time I was doing that?

Acting like nobody should notice you is its own way of getting nobody to notice you!  Security noticed you, of course, but they identified you as Pilar Pineda.

How does Pilar invoke that specialability on purpose, then, if not by wanting to go unnoticed?

By invoking Cayden Cailean's domain, a little bit of which is now Pilar's domain too!  In particular His domain of getting so drunk you black out, and then waking up and finding yourself somewhere unfamiliar and thinking 'What the fuck did I do?'

...sigh.

A subjective moment later (though in reality it must have been longer) Pilar suddenly finds herself in a forest.

The beach, the ocean, and the repurposed stone fort where Pilar lived for four months, are barely visible from where Pilar stands.

...now what.

(A terror in her, that the next instruction is 'put on the artifact headband so you'll betray Asmodeus' -)

Next, Pilar goes on some proper adventures so she can become a more powerful oracle and wizard!

...what becomes of Pilar, after she's more powerful?

What becomes of Pilar, in the end?

Snack Service doesn't dare speak intentions that much out loud under the shadow of tropes.