If I understand RAW correctly the Arcane Trickster loses the +2 bonus to his INT from his magic item. He does NOT lose his skill points, just the INT bonus to his Knowledge checks, Craft, etc from the magic item. There's a 24-hour clause before the temp bonus becomes "permanent" enough to count. This lets you take off the magic item to sleep, bathe, seduce, etc.
You have to be wearing the bonus-modifying item 24 hours before you level in order to count the new INT on your new skills for that level. The bump is not retroactive to previous levels. It does stack with your Level 4, 8, 12, etc bump to the modifier.
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Permanent Bonuses: Ability bonuses with a duration greater than 1 day actually increase the relevant ability score after 24 hours. Modify all skills and statistics related to that ability. This might cause you to gain skill points, hit points, and other bonuses. These bonuses should be noted separately in case they are removed.
You lose the permanent bonus you need to remove those bonus skill points specifically. You need to keep track.
It is important to note that items like the Headband of Vast Intellect grant ranks in specific skills with those bonus skill points, you don't get to pick them other then when crafting the item yourself. Not all items do this so read their descriptions to know which is which.
As for retroactive skill points you can look Here:
All bonuses are retroactive when an ability score increases, be they bonuses to damage, to skill ranks, to hit points, to saves, to skill checks... all of them.
The headband of vast intelligence (the most common example) gives skill points equal to HD of the creature donning it into a fixed skill chosen when the item is created. This is exactly to avoid this problem, and also to avoid the possibility to reassigning the points just by removing the item and donning it again for 24 hours. It's a special ruling because it's an easily lost and regained bonus. It' safest and easiest to extend this ruling to every other permanent bonus to int from items.
If the int bonus is given by actual changes of the ability score (like level advancements, wishes and tomes) you get retroactive skill points as stated in the ability score section.
Curious thought just occurred to me.
Aren't items like magic items that increase intellect "Double dipping"?
For every +2 f the item. your Intelligence bonus goes up 1, which auto adds into all intelligence skills as a stat bonus change. Then on top of it you get to add more ranks as well?
Isn't that kinda.. odd? Not quite right?
You don't get bonus skills from high int. The skill bonus from the headband is the bonus from the bonus to INT. Morgen linked to the FAQ for it, but here it is again.
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Not, what I meant.
What I was saying is, that you put the headband on. and when your Int score goes up. The attribute bonus goes up. IN the case we'll call it +1.
So mathematically speaking. Your Intelligence skills all automatically go up one point. Since its part of how they skill level if calculated.
THEN, you recalculate the skill ranks you got by level (+1 for each level), and you turn around and ad those new bonus ranks to the same Intelligence skill.
*Rereads FAQ* Hurmmm.. So Unless the item gives skills with it in its description. the bonus from the Int item doesn't effect the persons skill ranks at all? It only gives the inherent bonus to skills that the Int modifier gives??
Increases to Int do not retroactively grant skill points.
if you decide to put skill points into a skill that is gaining skill points via the head band you pick the better of the 2 as the skill points gained from the headband do not stack.
Increases to Int do not retroactively grant skill points.
Increasing Intelligence with the points you get every 4th level, or from inherent bonuses like those granted by the various Tomes, do in fact give retroactive skill points. You also gain an additional language known.
3.X D&D specifically said they do not grant retroactive skill points, but Pathfinder removed that language.