Use of the Pensieve in Legilimency

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No: HPFGUIDX 72950

Something about Snapes use of the pensive during Harry's occlumency
lessons bothered me...

Presumably Snape was removing memories from his mind so that Harry
wouldn't be able to see them. But he obviously knows what it is that
Harry saw in the pensive, before returning the thoughts to his mind.
This indicates that there is still a memory in his mind. But, clearly,
those memories were inaccessable to Harry during the lessons (else
what would the point be)?

So the question to me is, what does the pensive DO? It doesn't seem to
REMOVE memories from a persons mind, but it makes those memories
inaccessable via Legilimency.

All of these questions were really raised previously when Harry sees
Dumbledore's memories in the pensive. (Dumbledore seemed to know what
memories Harry had viewed without having to put the memories 'back').
I just didn't think about it then, as the Pensive was more a plot
device to give us some information about past events. In OotP it took
on more significance.

But in any case, it really isn't clear what the Pensive does at all.
Any insights?