Filthy TA picker here. 2.5k MMR, 65% winrate.
Ahem. -taps mic-
GANK HER. GANKHERGANKHERGANKHERGANKHERGANKHERGANKHER
I swear, almost 100 TA games in the past few months and I've been ganked mid like 6 times. As a result, I crush my lane, (TA can crush any matchup at 2.5k btw--Shadow Strike is one thing, but fuck it, Psi Blades hurt) have plenty of time to stack ancients, take the stack by 9 minutes with my insane XP advantage, get deso at 14 minutes, flashfarm, 6-slotted at 25 minutes.
Hell, just a few days ago I went 16-0 clowning with Deso-Moonshard-Rapier just because the team I was facing was so lazy in stopping me that it didn't matter what I built as long as I had damage (The match in question--it's a fucking clowntown game though, be warned. Really, TA is insane if no one bothers to stop her.
TA preys on two things: Complacency and stupidity. Always remember she is not strictly a ganker, and not strictly a farmer. If she falls behind at a point where she has at least one or two cores already (worst of all Deso) SHE WILL CATCH UP. In this way, she preys on complacency, in that most people will forget about her if she doesn't show for a while. In regards to preying on stupidity, always remember that, if she has Blink Deso, she can jump to anywhere in a 1200 radius and immediately drop about 400 damage. So think about it. Look at your situation and ask yourself: is there somewhere within 1200 units that TA could come from, and if she did, could I survive 400 damage followed by 200 damage auto-attacks? If the answer is no, you probably want to consider NOT BEING THERE. And remember, if you're farming, she can probably see you. Any TA worth her salt who's ahead will have traps all over your jungle.
Oh yea and if you forget about her she'll probably take Rosh. And if you try to take it, it's pretty much guaranteed she can see you doing it.
So, we've got her strengths. What are her weaknesses? Well, she can attack six times, and can be hit six times. As a result of the first part, she needs to build a ton of damage items to ensure that she can always do an entire hero's worth of health in six hits, leaving little room to build tanky. This means that, while her agi gain will give her decent armour, that's basically all she's got going for her. Break her refraction and she's no tougher than a support.
Her attack range sucks, meaning she's going to want to be right in the middle of the fight. To do that, she has to use blink, her only good escape mechanism, to initiate, meaning that unlike Storm or QoP, once she's in, she's committed to whatever batshit crazy bullshit she's blinked into. This in mind, BAIT HER. If you have a pretty good idea that she's trapped your jungle, or better yet, you've used detection to find her traps, don't just kill the traps--leave them there, have one hero stand on top of them and farm like nothing's the matter, and have a hero nearby to jump her when she jumps you. Even if you can't manage that level of co-ordination in a pub, at very least just don't be alone. Any sort of stun or slow will fuck with her really badly, as she needs to stay mobile. Buddy up, make sure one of you has one of those things.
TA is not nearly as strong as people make her out to be. When I play against people who can actually deal with her, she's practically useless. But when people don't know how strong she is, I can get out of control by 25 minutes.
PS: Also if you draft a pushing lineup and take away her map control early TA can't do shit. Not saying that's really an option in the kind of games TA will be stomping, but it is one other way to shut her down.