They don't go after your items. What the heck are they going to do with it? Take the time to list it on the marketboard for sale?
Nah, what they are after is your gil and to see if you are in an FC with access to the FC's gil too.
They use the victims account to log into the game with the hacked account, world visit to another server and send mass tells of the same luring statement that the poor victim clicked on prior. This is usually after they have wipe you clean of gil and maybe the FC's gil too.
This is an RMT operation to steal easy gil to offer up for sale to players who could care less how they come by their gil in game, even if it's breaks the ToS.