My cat, ironically also named Mittens, went through some bizarre behavior after her "outside" priviledges were revoked...

Quick story - I used to take her outside to allow her to sit and scratch on a wooden fence post, which she was quite content to do for a while. Until one night she decided she would leap off, so she did. After some coaxing with treats, I got her back into the house, and she's been an indoor cat since.

But for a few months following this, she would stand by the door, and literally scream at it to open. She'd also try pulling it open by sticking her paws underneath and yanking on it. Of course, she didn't limit these actions to just while I was awake - it could go on all day. She would also take to simply falling limp and whining at me, which I always took as signs of sulking - which is what it sounds to me like your Mittens is doing now!

She stills occasionally likes to stand by doors and wonder if she might be allowed outside, but the sulking has stopped!