How long have you had him?
Mine did this for about the first week I had her (trying to get out, digging) but soon she stopped both behaviors altogether.
She was 3 months old at the time, and that was 2 months ago.
I suppose you just have to put him back and teach him that when you put him away, he needs to occupy himself with his toys/food/etc.
good luck with your Grey.. sounds like a lot of fun with your flighted CAG. Mine was clipped when I bought her unfortunately.