Not that Katherine would've had any objections to an escort back to her room, but you have to ask if there was really anything to be concerned about.  Well...there was always the chance that a drunken soldier could bump into her and cause an incident.  The question, though, is who would be causing more harm to [i]whom[/i].  On the one part, you have such behavior being reminiscent of Kate's father, the reason you don't ever see the girl in any sort of drunken celebration.  It would very clearly make her uncomfortable.  On the other part, therefore, someone trying to give her a hard time might trigger a response that was bound to be [i]violent[/i].  Imagine the report on Erwin's desk for such an incident:

Wall Guard A gets tanked after Battle of Trost, remains in drunken and generally festive mood for hours.
Encounters Kate Bellows.
Guard A says something he presumes to be a proposition to Kate that makes Kate visibly uncomfortable.
Kate recoils, decides she wants to be anywhere else right now.
Guard A insists, makes a grab for Kate.
Guard A then wakes up a few hours later and picks up own teeth off of the ground, complaining of a massive hangover.

Yes, that would look [i]great[/i] on a report, and even the unflappable Commander Erwin would surely have an eye twitch or something in reaction, given that both a man might be irresponsibly drunk, and that the girl who mainly designs things has stood there and unleashed enough fury to require said man to [i]count[/i] his teeth.  All of this was completely hypothetical, of course, but you could definitely see it happen at this juncture, so it was probably for best that Sara looked after Kate that night.

All that aside, we must plow on ahead with their journey to the castle.  Eren was feeling better, for having gotten out of that hole of a dungeon, essentially.  One thing that definitely kept Eren calm, despite everything, was that he knew these people were on his side.  Yeah, Levi was kinda' scary and Sara had no hesitation in beating him up, but both were clearly trustworthy, which in turn made the special services perfectly fine.  Kate was unsurprisingly quiet today, but [i]very[/i] surprisingly focused and poised for any sort of action as she watched over the [i]second[/i] cart like a hawk, having looked over its contents perhaps a [i]bit[/i] obsessively, like some of the things might get up and walk away in the interim.  She had those gloves on, the ones made to attach to blades to become the Titan-Shredders, and pretty much every soldier here would have access to same, though the one who had definitely mastered their use was her.

Everyone was wary of Titans on the way up.  You wouldn't think that there was any particular reason to be, since this was the area between Rose and Sina, but after the Battle of Trost...they couldn't take the chance that some wanderers hadn't gotten loose in the confusion.  That was the official reasoning, of course.  Credible, but the actual reason?  You had to wonder.  In any case, they reached the castle and ummm...they had to clean.  Seriously, Levi insisted that the base had to be dusted and possibly [i]scrubbed[/i].  You wouldn't think him some kind of a neat-freak, the way he looked, but then you can never tell a person by looks alone.  And as for where Eren had to sleep, well...you could tell that he didn't like the idea of being in another hole, which didn't amuse him [i]later[/i] when Hange appeared and literally stuck him in one.

[i]That[/i] was a tense moment.  They'd stuck him in a dried-up well, asked him to hurt himself to activate his Titan form, and...nothing.  For some reason, he just wasn't [i]able[/i] to.  It was frustrating, having something like this that you could say was [i]literally[/i] at his fingertips, and yet he couldn't reach it on command.  Why?  The [i]worst[/i] part, beyond the confusion and disappointment, had to be that he'd bitten his fingers raw in the attempt, leaving him in pain for hours.  So, here they were, taking a break to get some food, and he was left like this, trying to figure this out with no ideas from the technical side of things.  Currently, there was a debate between Hange and Kate over whether anything in [i]normal[/i] Titans accounted for this, but there didn't seem to be so.  Sara would probably have heard Kate equating all the regular Titans to sleepwalkers, though [i]nobody[/i] had any idea why Abnormals were so...yeah.  I mean, they walked like they had a malfunction, and were singularly-obsessed on a specific target.  It was weird.  Eren's titan form [i]acted[/i] abnormal, but he was markedly different, for sure.

Eren was kind of staring at his hand when Sara addressed him, and he looked up with a concerned and irritated at the whole affair while trying to eat.  He flexed his eating hand a little.

[color=8dc73f]"I don't know what it is.  I thought I hadn't been hurt [i]enough[/i] while down in the well, so that's why I tried so hard, but it was a waste of time...  I didn't like it down there, either.  It was almost like I could tell it wasn't gonna work, even before we started, but I really wanted it to and-"[/color]

He'd started to eat again, but in his frustration he'd dropped the spoon.  He reached...

[h1][b][i][color=f7941d]THOOM!![/color][/i][/b][/h1]

Total chaos.

There was a crack of energy and a thunderclap, like a freak lightning bolt had shot out, and a rush of steam where the table had been.  Everyone at the table Eren had been at was either flung back or jumped back, if they were able to.  Instantly, everyone - elite or otherwise - was poised for action, blades out and ready to take on a titanic...

...arm.

The steam cleared and there was this grotesque-looking appendage that Eren was now sitting on, and...it had a spoon in its hand.  Kate was as shocked as Eren at this point, who was wondering [color=8dc73f]"Why now...?"[/color], not aware at first that mostly everyone here was staring daggers at him.  Kate was shocked, at first, at the sudden transformation...but then she received [i]another[/i] surprise.  One second, Hange was standing right there, making sounds equivalent to a tea kettle about to whistle, and the next...there was sudden empty space where she'd been standing, as she ran full-tilt at the arm.

[color=a0410d]"[i]EREN!![/i]  Can I touch it?!  I want to know how it FEELS!!"[/color]

Of [i]course[/i] she wants to touch it.