Parrots are cichlids. Most cichlids like to rearrange the tank as they see fit. Thats why the gravel is ending up in piles because he/she prob thinks it looks better

. But seriously, thats whats happening. The parrot will pick up a mouthful at a time, spit it out, and go back and grab somemore. Some do it more than others but it is def a common trait among cichlids (NW's anyway)

Yep, spot on.
I've had cichlids that were mean to other people but not to me and I could do anything to the tank without any fuss. With most of them, if I messed with their gravel they would try attacking my hands.
I had one particular labiatus (red devil) and when I would clean the tank I moved all the plants to one side. He was particular fond of one plant and it had to be EXACTLY in this one place. Well, I would move it and before I could vacuum there, he'd go get it and move it right back. We'd go back and forth 3 or 4 times until he'd get so mad he'd guard it and shake his body at me if I came close to it. He was a great fish.
It's their territory and they'll let you know when your decorating skills aren't good enough.