Jack will tell her he's pretty sure he could boot her out into SOME other universe, but he couldn't really guarantee which, so that would be a bad idea. He IS actually pretty good with interdimensional relations, though, so even if she is sort of a jerk he will tell her he'll work on a way to do that for her, and will be doing so in good faith.

He's travelled between dimensions before himself, but that was to alternate universes where a version of himself had existed, and it would be too risky to try the same stunt with her if they didn't have a guarantee of a connection.

MAGIC JARGON ETC ETC