The solution to this is to use a different escape sequence than C-a on the remote machine, or on your local machine. I put escape ^Ww in my local .screen

The solution to this is to use a different escape sequence than C-a on the remote machine, or on your local machine. I put escape ^Ww in my local .screenrc, and this alleviates most if not all the problems with running screen on both the local and remote machines.