Erfworld 66: page 60

[SteveMB]

I suspect that she wanted to at least send Ansom an "I must return now, I have vital intelligence." I suspect also that Webinar, who trusts her as far as he can throw her and her Gwiffon together, sent a somewhat shorter version.

If she'd told Webinar that, he would have (perfectly reasonably) asked her why on Erf she hadn't sent a report immediately when she first got the hat back.

Completely unsupported speculation follows:

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It's possible that the hats are not considered sufficiently secure, notwithstanding the fact that "they use codes". If Wanda wanted Jillian to think that she needed to report in person ASAP, she might have "let slip" that she has a way to read hat-o-grams (which would also provide an alternative explanation of how they're able to keep finding Jillian so easily, making it less likely that they'll figure out the Eyemancer setup).

So no, i don't think she's got any useful info to tell Ansom... if she did, she would have said she needed to report to Ansom rightaway, and not make up some lie about protecting the column; she's got nothing to gain from such a lie...Whatever Wanda said, it was probably nothing that Jillian thought was of any use

This may be related to the question of why she is either lying or repeating a false memory about how she escaped ("Through the tunnels, I told you."). Some more speculation:

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If she believes that Wanda is actually acting against Stanley, and is feeding her information and then breaking her out of the dungeon on her own initiative, she would lie to protect Wanda (both for obvious pragmatic reasons and because of the "subtle control" of the psychological bond she has developed). If she believes that nobody else in the Coalition (up to and including Ansom) is aware of Wanda's "betrayal" of the Tool, this would also entail lying to everybody on her own side.