Yes.  Please.  That would be fantastic.  What does she need?  They're thrilled to pieces at the idea of not having metaphorical unexploded adorable ordnance all over San Diego.

(Yeah, she also would like that. Very much so, actually.)

She needs a tranquilized specimen and a destination for her and her guiding partner.

Tranquilized is a problem.  Would immobilized be sufficient?  They don't have tranquilizers that'll reliably work on(instead of kill) a specimen, but they do have industrial strength zipties and gauntlets with which to apply them.

She needs to be able to safely touch it for an extended period of time during which she won't be paying much attention to her senses. She is agnostic to the particulars of the solution as long as it accomplishes this.

A teleport is rapidly authorized for a nearby commandeered you-store-it storage facility Official DRT Monster Storage Secure Facility.  Complete with armed and extremely armored guards, one of whom has bright pink hair.  It's not long before a moderately zip-tied and extremely caged unicorn giraffe is set up in a storage room secure holding cell for Causal Web's psychometric pleasure.

(It's a risk that the strain will kill the giraffe, but not that much of one.  Dungeon monsters are generally hardier than you'd expect, and if they trade one admittedly adorable unicorn giraffe for the city of San Diego, that's a great trade.)

Excellent! Causal Web and her guiding partner will accept the teleport.

Once she's in the warehouse, she gives the people there the same spiel about interruptions, how long this will take, and such. Any questions or things she needs to know before they get started?

These are the signals to slowly back off.  This is the sign someone needs to get the monster away from you.  This is the sign to give to kill the monster, but the monster is worth between five to twenty million dollars so please be responsible with it. This is the protocol...

There isn't a lot of protocol but it's extremely important to be safe with a dungeon monster.

(These instructions are mostly for the professional guide, since Causal Web is going to be Occupied, but Sam is capable of absorbing and acknowledging protocols!)

Then it's time for her to Approach The Monster.

It's making cute sad whinnying noises about being trussed up.

Yeah, well, it would, wouldn't it. 

She plops a chair in arm's reach of it, sits down, and reaches out to touch its fur.

(The giraffe was [seized|lured|trapped] by [Kuroko|the DRT liason|a civilian] <= a [bystander|sensor|drone sweep] reported -)

- it doesn't matter. None of this matters. 

Causal Web stops touching the giraffe, her hand and arm going limp.

Her partner looks at her closely, sighs slightly, and then coaxes her mouth open for makeouts. 

Well.  That's...kind of creepy-looking?  But we're all professionals here, we can pretend to be otherwise occupied while anxiously waiting for the report.

Hopefully they find this portal pretty quickly.

The next update they get is about twenty minutes later and it's "This one might take me a few hours." 

"And you can't be interrupted for any of it, correct?"

"That's correct, though I should have status updates for you before then," Causal Web says, doing her best to keep her frustration out of her voice. (Her best isn't bad.)

Resolute nod.  "Okay.  We're ready for you whenever, ma'am."  Being stuck on guard duty for an esper who can't protect herself suuuuuuuuuuuucks.

well, she's not enjoying herself either it's important, though. 

Back to it - slower and more carefully, this time. The web branches a lot more than she'd been expecting. (And Jenny isn't here, so she can't just brute-force it.)

About a half hour later (including some more makeouts, though this time Causal Web is at least a bit involved the entire time), there's a status update, of sorts. "Really wide range. Think I'm converging on the coastline, not yet sure."

"Got it."  She puts in some extremely preliminary findings in a groupchat, then takes the initiative to swap out their guards. 

Pink-Haired Guard is going to ask for a few minutes to visit the little esper's room, if Causal Web is okay with the girafficorn being taken away while this happens.

This is a good time for it - she needs more guiding before she gets zero'd out.

Pink Hair returns.  The changing of the guard wraps up.  Everyone's ready for Round Three of guarding a VIP from a tiny girafficorn.

Back in she goes, then.