Considering its price and provenance, the amulet of grappling should probably activate automatically when a theft is attempted
For perspective, the first ability of the amulet of grappling (né the hand of Abendego) is usually worse than just having a once-per-day command word activated magic item of an effect like the spell interposing hand. (That is, a wizard's CMB is usually terrible, and a fighter that specializes in grappling will pity the 1d4 points of damage the amulet's grapple deals. Although, admittedly, the immediate action activation of the amulet is a nice feature.) It's too much to pay 20,258 gp for this item if its second ability either doesn't activate after the first ability's seen its once-per-day use exhausted or only activates when the first ability's already in use (the duration of which could be anywhere from 9 rounds to forever).
(As a unique effect, the Magic Item Gold Piece Values Table isn't much help in figuring out the item's piecemeal value, attempts at reverse engineer the item's price—for example, by multiplying the item's price by 5 for its 1/day effect—doesn't seem to yield workable results, either.)
Further, although it originally appears as the hand of Abendego in part 3 of the adventure path Council of Thieves, Pathfinder #27: What Lies in Dust, that text provides no more real insight about it (except insofar as page 56's layout looks really tight, the hand's text maybe having been forced into the available space). However, seeing as how the adventure path is named Council of Thieves, an item that only chokes out potential thieves once per day is probably too little too late.
(As an aside, the item's original name comes from the Eye of Abendego, a permanent hurricane in the world of Golarion. It makes sense, I guess, for an item named after an unceasing windstorm to strive to keep all things near it. And, no, I have no idea why a Golarion phenomena's named for one of the Bible's fiery furnace figures.)
Entertain a house rule that says the amulet instead just deals damage
Even the first power of the amulet of grappling is problematic. Can the wearer move normally while the amulet grapples? Can the wearer drop the amulet off a cliff while the amulet's grappling someone and have the grappled foe plummet to its death? Rather than having these arguments—in addition to the one about how the amulet works at all—, simply let the amulet's wearer activate it as an immediate action once per day to deal 9d4 points of damage to a creature adjacent to the wearer. Also, have the amulet activate automatically any number of times per day to deal 9d4 points of damage both to any creature that attempts to swipe something from the wearer and to any creature adjacent to the amulet (including the wearer) that tries to swipe something. (I picked 9d4 because that seemed a sufficient deterrent without being high enough to try to exploit the amulet as a main attack or something. The GM could add a Reflex saving throw (DC 17) for half damage and even type the damage (I suggest electricity) if that makes this more reasonable for the campaign.)
Such a modified item'll provide a reasonable once-per-day attack, deter thieves, and avoid strife at the table.