Scenario 1: You're playing v. EtF. They've just scored their second 3/2 from hand with a San San behind a Tollbooth. And it's only their sixth turn. You've finally got your decoder up and running. This is going to suck you think, but you bite the bullet and make the run. 12 credits gone, but you got rid of that stupid San San.
EtF responds by installing another ICE in front of Tollbooth, clicking for a credit and then playing Friends. San San is reinstalled and an Adonis Campaign for good measure.
Scenario 2: This time Gagarin is your nemesis. You decide to check the new remote they just created. And it's Jeeves. You think, "I really can't afford to trash it, it'll set me way back. But if I don't, they are going to get some easy points. And I have already spent the credit to access it." So you trash it.
Gagarin calmly does much the same as EtF. Jeeves is reinstalled and a Commercial Bankers Group for the heck of it.
Would these scenarios bother you? More likely they do bother you now. This card is finding place in countless decks. Someone, for some reason, thought it would be okay to put only one pip on this card. A card that is incredibly versatile and powerful. Cards in archives are supposed to be hard to retrieve. Sure there are ways to get them back. Shuffle 'em back in with Jackson or Preemptive Action. Or spend two clicks to retrieve and then play a card with Archived Memories (a card that costs two influence).
So, yeah, I don't like this card.
Now onto counters to it. The following can be effective. Archives Interface, Salsette Slums, Imp, Edward Kim: Humanity's Hammer, and Wanton Destruction. All orange cards. Good cards, but not easy to slot into just any deck.
EDIT: Forgive me if I'm beating a dead horse, but I am getting more and more annoyed with this card. In addition to the above strategy of reinstalling powerful, high trash cost assets and upgrades, I am seeing another all too common scenario. On Jinteki.net I am seeing a lot of Asset Spam 2.0 decks. I will say that the asset spam decks of old, while sometimes annoying to play against, were perfectly legitimate. The corp would try to overwhelm the runner's economy and time with plenty of must-trash assets while sneaking out a point or two when they could. FiHP takes this to a whole new level. I'm seeing Gagarin and RP decks with FiHP, Clone Sufferage Movement, and a combination of the following: Museum of History, Encryption Protocol, Bio-ethics, Hostile Infrastructure, Jackson Howard, Preemptive Action, Mumba Temple, Tech Startup, Mumbad City Hall, Mumbad Construction Co. and more. Between clicking for money and making runs to trash, there isn't even time to draw cards, much less make runs with intentions to steal an agenda. I'm going to go ahead and tell anyone who is reading this, that if you are doing this, please STOP! It is not a legitimate strategy. Will you win? Probably a lot, Against me, you'll win by default as I will end up conceding after 20 turns of horrible monotony. But deep down, you must realize you are taking advantage of an obvious mistake that FFG made. It is similar to people still running the Au Revoir, Turning Wheel, Snitch combo. Or the DDoS, False Echo, Hyperdriver combo. You know it is broken, so stop doing it.
And last thing. This is one of those cards that demand that every runner, for the foreseeable future, build their deck with counters to it (much as corps must build around Sifr at the moment). Cards like that may be fine in and of themselves (this one isn't) but they should all cost a lot in influence so that at least you don't have to run into them every single game.