the lord of the rings - When did this "Great Siege" that the orcs talk about in this dialog happen?

An extract from the Two Towers - The Choices of Master Samwise

At this point Sam began to listen more attentively and pressed his ear against the stone.

'Who cut the cords she'd put round him, Shagrat? Same one as cut the web. Didn't you see that? And who stuck a pin into Her Ladyship? Same one, I reckon. And where is he? Where is he, Shagrat? '

Shagrat made no reply.

`You may well put your thinking cap on, if you've got one. It's no laughing matter. No one, no one has ever stuck a pin in Shelob before, as you should know well enough. There's no grief in that; but think-there's someone loose hereabouts as is more dangerous than any other damned rebel that ever walked since the bad old times, since the Great Siege. Something has slipped.'

What is this "Great Siege" the two orcs are talking about?

Answer

The siege that ended the War of the Last Alliance, and the Second Age, was called The Great Siege and is also explicitly referenced as such by Tolkien:

"the Second Age ends with the Last Alliance (of Elves and Men) and the great siege of Mordor"

_{Letter 131}

I would say it's safe to conclude that this is the Great Siege of old that is being spoken about. The siege started in SA 3434 and ended in SA 3441 along with the Second Age. This conversation was in TA 3019, meaning the siege was 3026 years before.