There are two aspects to the feature. There's not a setting to disable that one. I've disabled the setting that does exist but the while-you-were-away version of the feature persists.

It's disabled in settings. They periodically re-enable it, it's a very user-hostile behavior.

I'm going to expand on this. There are two distinct annoying features.

1. The one you're talking about, messes up the chronological order of the timeline completely. That one is called "Show me the best Tweets first", in settings, and I have disabled it. Some people report Twitter flips the switch whenever they see fit, but that has never happened to me.

2. The second one is a small widget that appears at the top of your timeline that says "while you were away" and shows three tweets. There is no way to disable this. This is what it looks like on a desktop: http://i.imgur.com/R6rPRGo.jpg There are similar ones for mobile. I don't personally care too much about it (I close it... just one of hundreds of annoyances I have to put up with when I use a computer) but there's a huge problem: those three tweets are removed from your timeline, wherever they were. So they mess my timeline up (someone might have tweeted two things in rapid succession, and one of the tweets goes missing because they move it up to that widget). And there is no way to disable this, at all.

I believe that even when you dismiss the recent tweets box, the tweets still don't return to your timeline.

It's baffling bad.

Yes exactly. It's embarrasing. Those tweets are just removed from your timeline and there's no way you can make them return. For someone like me who follows just a few people and intends to read the entire timeline, it is very very bad.

That's their core product there and it's broken. And they don't care. I miss the twicca days... That's the Twitter I liked, a chronological stream of text. I mourn for it.

It's also one of very few changes I've seen (one of which was changing the icon and word for the favorite/like action [which was a breaking change as far as I'm concerned; it changed the semantics of past discussions and eliminated the personal bookmarking aspect]).

I cannot imagine what Twitter is spending its time doing.

Twidere for Android is a great client that respects chronological ordering, saves your previous position, and doesn't show ads. I don't know of a desktop solution. I just put up with their shitty website and avoid it whenever possible.

There's no way to disable that feature.