There's an observation window full of tourists with cameras, who are on a guided tour of the publicly-accessible areas of the Hall. They excitedly snap pictures of the sidekicks through the glass, especially Karen. She might not be doing anything particularly fascinating right now, other than floating, but she's new and therefore inherently interesting. 

"...quick debrief to discuss the coincidence of four ice villains attacking on the same day," Batman is saying quietly to the other mentors.

"We shouldn't be long," he adds to the room at large. 

She is really really glad her ring had the - foresight? does the ring have enough agency or predictive ability that it can be said to have foresight? - to give her a full face mask. It's handy for making it easier to pretend that you aren't internally really nervous every time you remember the cameras. Cameras are honestly the worst part of all of this, by a lot.

She waves at the tourists and waves at the other green lanterns as they leave. 

One by one, the adult superheroes stand in front of the door marked "Justice League Members Only" as blue light sweeps over them from head to toe.

"...GREEN LANTERN, ZERO FIVE. GREEN ARROW, ZERO EIGHT. MARTIAN MANHUNTER..."

"That's it?" Speedy demands.

"You promised us a real look inside, not a—a glorified backstage pass!"

Oh dear. She's not getting involved in this argument, though, she doesn't even know Speedy.

"It's a first step," Aquaman says to Speedy. "You've been granted access few others get." 

"Oh, really!"

Speedy points accusingly at the tourists behind the viewing window, who are resisting their guide's attempts to move them on in favor of snapping pictures of the confrontation. 

"Who cares which side of the glass we're on?"

So on the one hand Speedy is right, it's a bit silly to treat this as a more important step than, say, being granted access to the League training facility in Nevada, but on the other hand if the League doesn't want them involved in more central aspects of its organization then that seems like the League's choice, and the really important bit is the bit where they stop people from hurting other people, which seems pretty unrelated to whether they get to be in the Hall of Justice or not.

But she's not volunteering any of those thoughts right now. Nope.

          Green Arrow steps forward to defuse the situation. "Roy," he tries, "you just need to be patient." 

"What I 'need' is respect," Speedy snaps back. He turns to the others. "They're treating us like kids—worse, like sidekicks! We deserve better than this."

The other boys look at each other awkwardly. 

"So what if they don't respect us," says Karen, now that the rest of the group has been addressed. "Batman, Superman, the other green lanterns, they were all helping people way before the League existed, way before anyone knew to thank them. They don't do what they do for respect or acclaim. The whole Hall of Justice monument thing is - if it's dumb it's dumb because respect isn't the important thing, accomplishment is."

Aqualad nods thoughtfully. Robin and Kid Flash make noises of agreement. 

Speedy doesn't look so convinced. He rounds on Karen in disbelief. "You're kidding me, right? Of course it's dumb. This whole thing is one giant distraction from what's really important. You're right," he continues. "The Hall doesn't matter—because it isn't the League's real HQ! It's just a false front for tourists, and a pit-stop for catching zeta-beam teleports to the real thing: an orbiting satellite called the Watchtower!" 

There are gasps from the Leaguers behind him. 

"So?" asks Karen, hoping that she's able to hit 'completely unimpressed'. It's easier with the face mask. "If all you care about is a sufficiently fancy backstage pass, then maybe you don't deserve to be a League member."

- oh frick oh frick oh frick all the sidekicks are going to think she thinks she's better than them now, frick -

"Don't you get it? They lied to us!" Speedy turns to the other kids. "I bet none of them ever told you about the Watchtower, huh? Did they?"

One by one, they shake their heads.

"See? This isn't about prestige, it's about trust. And they don't trust us. This proves it. If they couldn't even tell us something as basic as where the League is really based—" 

"Wait a minute." Robin looks shaken by the revelation but seems to be recovering from the shock faster than Kid Flash or Aqualad.

"How did you find out?" he shoots back at Speedy, adding, "And why should we believe you?"

"Good question," Batman growls.

He aims a glare at Green Arrow. "How did he find out?" 

Green Arrow looks sheepish. "I know, I know, but I thought maybe we could make an exception?" 

        Batman's eyes narrow even further.

"...or not." 

Karen is genuinely less shaken than the others; the green lanterns have their base of operations on another planet, so it's not a very big update that the League has theirs in space. She could probably fly up and find the Watchtower, eventually, though she'd have to have some idea where to look, because space is actually really big. 

She doesn't say any of this. She kind of wants to fly out a window somewhere and be alone with her thoughts, because this is - dumb, actually, Speedy's not wrong, it's a consolation prize that reveals a fundamental misunderstanding of why she, at least, is here. He's handling it completely wrong, but he's not talking nonsense.

But it'd be wrong to leave the argument like this, and it would be wrong to keep yelling in front of the tourists. She flies down and lands just in front of Speedy.

"One of them trusted you, before today," says Karen, quietly. "I think right now the others are feeling like they were right not to."

He looks away and doesn't reply. 

(The tourists are no longer watching, having finally been persuaded to move on by their harried tour guide.)

She probably shouldn't have said that, even if it sounded cool. She doesn't know Speedy; there's not much reason for him to listen to her.

She'll fly back up again and stop giving him a hard time.