To be fair, there is no evidence that CIQ is "breaking the HTTPS handshake". The article I read implied that the software had access to keystrokes, which could be used to infer data that would be encrypted on the wire, not that it was breaking HTTPS.

It's possible that CIQ is getting keystroke information, but only storing metadata (character counts, number of corrections, etc). But, without more evidence, it's best to be wary. I think John raises a valid point; crack open a debugger, disassemble the .dex, start a network sniffer. Find out what is happening, don't just assume.

Edit: fixed minor typo.