An online dictionary adds to the definition of “pica” ….
“pathological craving for substance unfit for food” (such as chalk), 1563, from M.L. pica “magpie,” probably translating Gk. kissa, kitta “magpie, jay,” also “false appetite.” The connecting notion may be the birds’ indiscriminate feeding.
In fact, the bird’s scientific taxonomy is “pica pica”.
Magpies are considered thieves. In folklore, magpies’ penchant for picking up shiny items is thought to be particularly directed towards precious ones. Could that be what’s going on in ecclesiastical pica? A bunch of episcopal magpies trying to pick up shiny, precious objects (in this case called “parishes” and “dioceses” and the tithes and offerings of their members)? Some have suggested as much, but I would not be so cynical as to do so….