The obvious guess is that Harry will destroy the Dementor in full view of everyone. But this seems far too obvious for Eliezer to taunt us so.

Harry knows nothing about the aurors, the Prophet reporter, Umbridge, Fenrir Greyback (if that's a correct identification), or Amelia Bones.

That leaves

• The dementor
• Minerva
• Lucius
• Neville's grandmother
• Himself

The dementor he can destroy, but that's the obvious answer. Minerva he knows nothing shocking or incriminating about, and I can't think of anything that would help. Same goes for Madam Longbottom, I think.

That leaves

• The dementor
• Lucius
• Harry himself — Oh, and I forgot: Everything in Harry's pouch.

What could Harry say about himself that's shocking? He could confess to his role in the Azkaban breakout, but I can't see how that would help Hermione. None of his scientific knowledge or magical discoveries would impress the Wizengamot, if they could even understand him.

Does he know anything incriminating about Lucius? Well, he knows he was a Death Eater. But Harry is immune to Veritaserum and can't testify.

Is there anything he can do about or with the dementor other than destroy it, which is far too obvious?