I saw the title, got ready to post about my own criminal monkey misadventures, and realized it's the same place (Uluwatu Temple). However, the story underplays an important element: it's actually a triangular syndicate of crime, and humans are very much part of the picture.
First, the monkey steals something of value from a tourist and (the missing bit) they run inside the temple buildings, which are off-limits to tourists.
Second, a friendly temple priest or caretaker (the mentioned "monkey handlers"), who is allowed inside, fences the loot by exchanging it for something a monkey values, like a tasty banana.
Third, the relieved tourist gets their belongings back and generously tips the caretaker.
First, the monkey steals something of value from a tourist and (the missing bit) they run inside the temple buildings, which are off-limits to tourists.
Second, a friendly temple priest or caretaker (the mentioned "monkey handlers"), who is allowed inside, fences the loot by exchanging it for something a monkey values, like a tasty banana.
Third, the relieved tourist gets their belongings back and generously tips the caretaker.