The annoying part of all this is that Billie's suggestion makes sense. Because not only is this place suspicious to walk in and out of, Strange himself doesn't fit the place in the slightest. Nobody looks at him and thinks 'blacksmith' and he knows it.

"I know, I know," he sighs, as if this is a major inconvenience. "The problem here is that I'd want to take Bell with me and the spell only covers one being."

So it's either him leaving visible or a hare leaving visible: both kind of obvious in their own ways.