、。
Strange to say, she knows all about it.
Literal
Strange story but [concessive-が], she [topic-は] that matter [object-を] very well knows.
妙な話だが is a set frame meaning 'strange as it sounds,' 'odd to say.' が here is the weak concessive 'but,' linking the framing to the main clause rather than marking a subject. 知っている ('knows') uses ~ている in its resultative sense — 知る ('to come to know') + ている = 'is in a state of having learned,' hence 'knows.'