My wife wrote him when she was 5 as part of a class project. They got this return letter shortly after.

I've done some research and cross examination online and think there is a reasonable chance it is his autograph. I don't think it is autopen because the transition from the r to the t in Carter isn't even. I don't think a secretary signed it because her t is more upright and her r is different. I'd be a really really nice piece if it is authentic. Any thoughts would be appreciated. Thanks