Primarily, the cause of ick is STRESS. It is a parasite, that healthy fish can typically keep in check. But once stressed, it can be a problem....much like we are surrounded by germs but really get ill after a stressful period.
That stress can be water quality, poor diet, too much variation in temp and other params, aggression, small tank, shipping, etc, etc, etc.
The really critical point is removing the STRESS source. Even if you took the fish, treated them, left the display without fish so the parasite died off...and put them back in, the stress would likely result in other diseases or issues or death.
In any outbreak of disease, IMO, you must address the root cause. Honestly assessing what is wrong with the tank (and very very commonly it is overstocking or overly aggressive fish) is a crucial step.
Keep in mind, too, that fish from an LFS are in a highly stressed state. They are "new" to the captive world, shipped here and there, with a new strange diet and no place to hide, and in small enclosures with fish they might not otherwise be around. If you take this and plop it right in your new tank, odds are fairly good you might have a problem, just from lingering issues alone. Then the fish is in another new system, with new fish that may not want it there, etc, etc, etc. Bam, ick.
The only true treatment to kill the parasite is copper or hyposalinity, IMO. But the parasite may merely be a symptom of a more significant issue.