People who make prophecies don't remember them. We see this as early as Prisoner of Azkaban.
‘You – you just told me that the – the Dark Lord’s going to rise again ... that his servant’s going to go back to him ...’
Professor Trelawney looked thoroughly startled.
‘The Dark Lord? He Who Must Not Be Named? My dear boy, that’s hardly something to joke about ... rise again, indeed ...’ (PoA, Ch. 16, Professor Trelawney's Prediction)
Dumbledore straight up tells Harry she can't remember the prophecy
I cannot ask Firenze to return to the forest, where he is now an outcast, nor can I ask Sybill Trelawney to leave. Between ourselves, she has no idea of the danger she would be in outside the castle. She does not know — and I think it would be unwise to enlighten her — that she made the prophecy about you and Voldemort, you see." (HBP, Ch. 19, Elf Tails)
And Professor Trelawney even gives her own (prophecy-less) recollection of the night.
I well remember my first interview with Dumbledore,' went on Professor Trelawney, in throaty tones. 'He was deeply impressed, of course, deeply impressed ... I was staying at the Hog's Head, which I do not advise, incidentally - bed bugs, dear boy - but funds were low. Dumbledore did me the courtesy of calling upon me in my room at the inn. He questioned me ... I must confess that, at first, I thought he seemed ill-disposed towards Divination ... and I remember I was starting to feel a little odd, I had not eaten much that day ... but then ...'
'... but then we were rudely interrupted by Severus Snape!' (HBP, Ch. 25, The Seer Overheard)
You mention Legilimency and the Pensieve, and that's something to that. Dumbledore, after all, is able to extract Morfin Gaunt's memory of his encounter with Tom Riddle that way. But in that case, there was a true memory that had been magically altered waiting underneath. Every indication is that Trelawney never formed any memory of the prophecy to begin with. And more to the point, Professor Trelawney lives under the constant protection of Dumbledore, making it difficult if not impossible for Voldemort to get at her.
Or put another way, if it were easier for Voldemort to get the prophecy from Trelawney rather than the most secure section of the Ministry of Magic, don't you think that would have been his plan?