The marked pit is a little south of the wall, at the south east corner of the temple complex, correct?
Did you already explore that area and find the statue (and a charm) on your own? The closed pit is slightly darker than the surrounding ground, with little else to indicate anything is there. Without the map flag, you'd most likely just find it by accident, if you happen to run your mouse cursor over it.
In any case, if you had opened the pit, a soldier would have approached and demanded the statue, claiming it was temple property. Sound familiar? You can refuse and kill the soldier, keeping what you found. If you hand the statue over, it can be found again in the warehouse, in the south east corner of the temple complex.