。
She told me about it in strict confidence.
Literal
She [topic-は] top-secret [in/manner-で] me [to-に] that talk [object-を] did.
極秘 (literally 'extreme secret') is heavier than 秘密 ('secret') — it's the term for top-classified, no-leak information used in military, political, and corporate contexts. The で here marks manner ('in a top-secret way' = 'in strict confidence'). The double-marked recipient and content (私に~を) plus the past-tense topic-establishing ~の話 builds the layered meaning of 'told me secretly about a particular matter.'