It's a rare thing when Nill wants to reach for people not to give them comfort - though that urge is near constant, more instinct than much else - but to find her own comfort. Anything like that is brief and typically brought about by fear or separation, or sometimes both. Like when she hugged Karkat after he'd been gone as long as he was after the last arena, or when she hugged Linden after it. While not a stronger urge it leaves a dull, numbing ache in her chest, and she can't act on it, won't. As much as she would love to hug him, or touch his cheek, or do much of anything she has no idea how much touch he can handle right now or how much worse the physical damage is where she can't see it.

She writes a new line, and hesitates just the slightest bit before hooking the pen onto the notepad so she doesn't need to hold it. Then Nill reaches for his hand, the one still at his side, and if he doesn't flinch or try to pull away she'll carefully lift his hand and place it against her own cheek, holding it there. If Karkat could do it without them getting into trouble, then surely she could at least one time.

thank you for protecting me.

As much as she hates to admit it, had Claudius succeeded in forcing her to come back with them she would not be handling it as well as Linden is, not even close. Nill only hopes that she can return the favor some day. It doesn't feel like she's ever succeeded at keeping Linden safe.