[DMCA]

Besides, I didn't say if I believed in telepathy, I just asked how it could be explained.

[millefleur]

One way some telepathy phenomena can be explained is by what the Bible calls "familiar spirits". In other words they are spirits that are familiar with a certain human and can communicate by interjecting words (thoughts) into the mind.
The Bible of course condemns encouraging this sort of interaction.
In the Old Testament there was an account of God causing a donkey to speak with an intelligible voice.

In this case a spirit could be at work with the parrot and the owner but not of God, simply to cause confusion and deception which God allows.