Hi there Fiona, I've had lots of people ask me this question and truth be told I'm not 100% sure why they do it, but lots of Greys do. I have a young Timneh, Darwin, and she has done this since I brought her home. She has a gajillion toys in her cage and is perfectly behaved, so I'm not sure it's out of boredom. I know of quite a few Grey owners who have mentioned that they do this, it's almost as if they're digging.
I would try not to worry too much about it as I think it is more of an instinctual thing than a behaviour issue. However continue to do what you are doing by not going to Bonkers and giving him attention when this happens, as that could reinforce it.
Hope this helps, and I'm sure many others will have more knowledgeable responses.