iterm2_shell_integration.sh injects strange control sequence into termite

This isn't related to iTerm2 itself, but rather the shell integration it ships with.

I have ~/.iterm2_shell_integration.zsh sourced on all my machines. When I SSH into those machines through iTerm2 or urxvt, everything is fine. However, when I SSH into one using Termite, I get a strange control sequence added to the beginning of every command's output: ]133;C;. Here's a screenshot:

The problem goes away if I stop sourcing ~/.iterm2_shell_integration.zsh or if I stop using termite, so I assume the problem is somehow related to the interaction between the two. I realize this is probably a bit out of scope for the iTerm2 maintainers to worry about, but you guys are terminal emulation experts and know the iterm2_shell_integration deeply, so I'm hoping you might be able to give me an idea of how to start diagnosing/debugging this.

Oh, and as far as I can tell, I do have a correct termite terminfo installed on my system.