There seem to be many misunderstandings though as to what it actually is or how it works both among the creative world and the fandom. So let's dive straight into it shall we?
In essence, it is a Pavlovian response to a scent that makes her react on pure instincts and muscle memory that best corresponds to the target it's used on. Her instincts take over and immediately implement how to end them efficiently without hesitation but also to best prolong her longevity; allowing her to move onto the next target or to complete the mission objective. She effectively blacks out all conscious thought and goes on pure killer instinct and strategic training. While many associate this to a berserk rage as that is the easiest way to allude to what exactly it does to her, it does not mean this subconscious response is without its own form of thought or analysis. As shown it is even more deadly, calculative, and precise with no restraint suggesting it creates an increased fight or flight response without the flight. As such her mind seemingly goes into overdrive about target acquisition to end result without any restraint towards whoever is marked in order of efficiency that also best provides her with the best survivability to move on to the next threat for rapid assessment and neutralization. Unlike a berserker rage, she is highly apparent and observant of bodily harm that can be taken during such acts and still reacts with avoidance as it would contradict the instinctual goal of ending the existence of the target or multiple targets marked.
In a mission for the Kingpin, Wilson Fisk, as he hired the Facility to use her, we're shown an instance of how she reacts to threat assessment for order of kills even while only one is marked with Triggerscent.
In the image above, notice she dispatches the two behind her before going towards the one marked. They could have hindered her progress so they are taken care of first. This suggests environmental awareness and mild cognitive strategic implementation to her movements. (X-23: Target X)
In X-Force v3: Not Forgotten, we're shown Laura using it in more strategic manners again. Not just with her implementation of it in the sprinkler system, but with her actual atacks while underneath the influence of it too.
Notice she goes straight for the head as she goes above. Seemingly planning her attacks as fast as she moves. While she does land in the middle of the security forces after this leap, she continues on strategically to take out their footing by cutting the shins of the security officers around her.
While she does take bullet fire as well, she still manages to dodge it to avoid major organ damage or anything more than grazed head shots as it would inhibit her progress. This further shows implementation of cognitive reasoning even while under the influence of it. Notice below, she only takes gunfire to the shoulders and her arm, avoiding the core body area from being hit.
In one such instance during the story. She goes so far as to use one guard as a means to scare the Facility Director that's on location. This also suggests some of form of awareness to her surroundings and as the sprinkler system switches to water, she shows no signs of location disorientation, only surprise that it's gone. This further suggests she was at least mildly aware of her actions which could also be in conjunction with how she intentionally used Triggerscent to heighten her aggression and adrenaline for this onslaught.
Over in her origin miniseries X-23: Target X, we're shown another such occasion of both strategic implementation yet also mild control of target order.
We're shown this when she ignores Megan who has been marked by the tea, to go after Desmond first instead even though Megan is closer. Threat assessment would dictate Desmond is the bigger problem to be dispatched first. Also from a strategic point, she could launch straight forward at Desmond which would give Megan an opening to escape as X-23 leaves the door behind her wide open. This would also seem to suggest the possibility of mild subconscious control even while in this state.
Triggerscent itself only works if Laura can smell it or in theory potentially taste it on the air(per the original programming she was exposed to it through both manners). Once it has dissipated or she cannot recognize it being present, the killer instinct fades almost immediately. Barring the reconstituted new formula as created in the ongoing comic's storyline Touching Darkness. During Collision the ongoing comic had used the original formula that Laura was raised with as the Facility created her to react towards, but in the story that followed, a new version was created that has a slightly different reaction as it works on chemical level that forces even civilians to react on a more primal level. This variation in essence has slightly different connotations and does not create the same complete conscious mind suppression that the original does. In effect, her healing factor can fight off the long term effects even with vestigial traces still in the air or on nearby subjects. We're shown her still under the effects of this new Triggerscent, and yet also to come to her senses before the effects have completely faded.
These dueling forms of how it was implemented into her life may have also allowed her a slight more controlled response to initial contact of any variation of the formula thereafter. On Arcade's island for example, we're shown Arcade is using his own formula based around the original Facility's usage of it as a way to awaken her killer instinct without restraint. His variation on the formula though may not be exact and may only have a slight delayed response as it could take a moment for X-23 to recognize the actual needed scent through whatever excess he is using. This could allow her a chance to respond or warn others before it could entirely kick in.
This further dilutes her Pavlovian nature to the scent though. Effectively the increased exposure to different variations over the long term should start to override the initial programming to it. It effectively "muddies" the waters of the original implementation.
There are several different potential methods to further dilute the response to the scent. One such method would be exposure and re-exposure to it under controlled circumstances where she cannot harm the one marked with it or in its presence. Another way would potentially be damage to the area of the brain where the response corresponds, allowing her healing factor to regrow the tissue that would effectively neutralize the neural pathways to that response. The "brain damage" method would only possibly be a short term solution though as the neural pathways may eventually reconnect. So a therapy manner of exposure and re-exposure to deprogram it under controlled circumstances would be the best method as we were shown as possible to work with Touching Darkness. Such a therapy would need to use diluted usage of the scent to increasing the potency to allow her to adjust slowly, but would also require those within the vicinity to be able to restrain or survive any such outburst that may occur. Kimura with her impenetrable skin as an example, or any teammate that could survive such an ordeal as vampire Jubilee potentially, Shadowcat, among anyone else that would have the means for avoidance or high survivability rate due to a healing factor or other form of defensive power that could prevent harm to themselves in the process.
One such example of a way to do this would be to douse Kimura in Triggerscent and let X-23 handle the rest. As X-23 cannot cut Kimura, X-23 could not kill her. Barring any reprisal from Kimura herself, over the duration it would effectively neutralize the effects of Triggerscent as she cannot complete the instinctual action as programmed. It would essentially dull the response over time. It may also create quite a therapy moment for Laura, but only if Kimura harming her back could be negated.