If it matters to you at all, removing the stopper would be "activating an item".
If we're talking about the spell invisibility, activating an item isn't an action that breaks invisibility anyway, so that's moot. That said, this rides close to the fine line between "opening the portcullis to let the attack dogs out" (which doesn't break invisibility) and just dropping a stinking cloud spell at your feet (which does break it).
I've gone back and forth twice on this one while typing this, so while I don't have a solid answer, I sympathize.
The condition that breaks invisibility is "The spell ends if the subject attacks any creature."
After that, there is a list of things that either explicitly do or explicitly do not meet the criteria of 'attacks any creature'.
This list is neither inclusive nor exclusive. In other words, just because something is not on the list doesn't mean it is necessarily either an attack or not an attack.
At that point, you have to use the listed examples and determine whether the specific action undertaken qualifies as an attack. Basically, the rule seems to be if you yourself cause harm (spell) it is an attack, but if you cause an external party to do the action (summoned monster, a trap) it isn't.
So that leads us to the question if the Discord Bottle is part of 'you' or not. In some ways it seems obvious that it is not, but for other purposes an attended items are considered part of the creature wielding/holding them and aren't considered a separate thing.
I think that considering magical items being activated as directly being actions of the creature to be more in line with the intent. So you toss a sphere from a Necklace of Fireballs toward a cluster of your enemies and that is an attack.
Discord bottle though doesn't even have a direct effect or area. It creates gas that expands to 50' in one round and extends further after that. The gas then causes negative effects. To me, this makes it removed enough that it would be an indirect attack, and therefore not break invisibility.
Attacks: Some spell descriptions refer to attacking. All offensive combat actions, even those that don't damage opponents, are considered attacks. Attempts to channel energy count as attacks if it would harm any creatures in the area. All spells that opponents resist with saving throws, that deal damage, or that otherwise harm or hamper subjects are attacks. Spells that summon monsters or other allies are not attacks because the spells themselves don't harm anyone.
I could see the Discord Bottle going either way. But since you have to save against the effect of the bottle, I'm going to assume that it is actually an attack, and so should end the invisibility.
Asmodean argument: Most traps offer saving throws, but you can trigger them without breaking invisibility.
Hmm. It actually says you can "remotely trigger traps". But what does "remotely" mean? You have to set the trap off without touching it?