No offense taken, apparently, since Alice doesn't look annoyed at the statement in the slightest. She gets it, after all. That's exactly what she thought when they spoke of her just being part of some dream beyond the looking glass.

"Alice," she instead replies to the last part, "Alice Liddell." There's little harm in giving away her name when this train loves to display it everywhere.

"And yes, I do. I suppose that depending on who you'd ask, some would call me mad."