- Q: How does Terrible Secret interact with cards like Ward of Protection (cancel), Delay the Inevitable (horror cancellation) and Deny Existence (horror ignoring) A: Terrible Secret reads: "Cannot be canceled." at the end of its effect. This means that any card effect which would cancel the card or any of its effects would fail (such as Delay the Inevitable). However, card effects which ignore the horror, such as Deny Existence, would still work, because it is not cancelling anything.
Madness.
Revelation - If there are no card beneath Diana Stanley, shuffle Terrible Secret back into your deck. Otherwise, for each card beneath Diana Stanley, you must either discard that card or take 1 horror. Cannot be canceled.

Doesn’t Deny existence only work on encounter cards and enemy attacks? I could be completely misunderstanding part of the interaction or encounter keyword- I’m still learning a lot of the technical side of the game
This is a very situational signature weakness. Looking at the two elements, the effect and the discard condition, we get:
The effect: Diana has to discard cards beneath her (reducing her and invalidating the Twilight Blade and her effect, otherwise, she has to take horror. The latter is somewhat fraught, as Diana is pretty average on Sanity, especially compared to other investigators. This can be bad, if you are playing a Diana who cares about or utterly irrelevant if you aren't. The horror cannot cancelled, but it can still be negated by Deny Existence.
The discard condition: One and done, unless the weakness will have no effect, in which case it gets reshuffled.
All in all, this is a below average signature weakness, way below if you have a Deny Existence in hand or don't care all that much about Diana's . Edit: if you really care about Diana's , this weakness's threat gets upgraded, although, as long as you can keep a Deny Existence in hand, it's extremely manageable.