I had the same issue with the CrashPlan.app folder located within the /.MobileBackups.trash after turning off local backups. I was not permitted to delete it. "rm -rf" on this directory did not work for me.
I had two problems because of this. My system log was full of errors regarding failure to delete the /.MobileBackups.trash directory. So if the operating system wanted to delete it and couldn't I figured something was wrong.
For a very long time there was no evidence of this problem except in the logs. Starting today it caused the icon in the menu bar to report failed time machine backups. The logs showed that the backup was successful but an immediate attempt to delete that trash file failed.
These two problems motivated me to take action.
I ran "ls -lO" and saw that the CrashPlan.app folder had the "schg" flag set. This sets the directory to "system immutable". Running "chflags noschg CrashPlan.app" removed this flag. I could then remove the folder with "rm -rf". I decided it was safe to remove this single folder since it related to an application specific file. Since the root level file "/.MobileBackups.trash" was a system directory I decided to leave it alone. I hoped that subsequent attempts by the OS would succeed.
I uninstalled CrashPlan and verified it was deleted from the Applications folder. I then triggered a time machine backup. The CrashPlan.app folder was reintroduced to the .MobileBackups folder. I got mad. I then decide to delete the trash folder. For me it's safe since I maintain two full clones of the boot volume on external drives.
After this the logs and time machine menu bar icon stopped showing the error.
Be very careful with the "rm -rf" command. It's so dangerous since you could delete a ton of stuff that could break your system. Make sure you understand the command.
As an aside, Linc Davis' comments were astonishing. They made me very uncomfortable and a bit afraid to post my experiences. I hope he doesn't respond to this post.