。
She caught what I was hinting at and smiled.
Literal
She [topic-は] I [subject-が] obliquely said meaning [object-を] grasped-and smiled.
それとなく言う ('to say obliquely, to hint') is the standard phrase for indirect communication — saying something without saying it directly. 悟る ('to realize, to perceive, to grasp [a hidden truth]') is a verb steeped in Buddhist resonance — it's the same word used for spiritual enlightenment (悟り 'satori'). In everyday use, it just means 'to perceive [something subtle].' The te-form chain 悟って...ほほえんだ links perceiving and smiling: she got it, and signaled her understanding with a smile. A culturally rich moment of indirect communication.