Attacks of opportunity and invisible opponents

[Bellberith]

So, if i reach through a canopy of a cart and grab somebody while invisible, then cast dimension door. Can guards inside the cart with their swords drawn make an attack of opportunity on me?

The way i reach through was through the cloth of the canopy. So a hand size hole did appear but it was all during 1 round.

[HammeredWharf]

Normally, you can't AoO something you don't know is there, so they'd have to make Spot/Listen checks. The curtain could give them a bonus to those checks at the DM's discretion. If they notice you, they're probably still surprised and flat-footed, so they'd need Combat Reflexes to AoO you.

Keep in mind that you can only use Dimension Door on willing targets.