How were you contacted? Did they phone you? If it was TFL, do you know how they got your number (Oyster registration perhaps)? How did they confirm who they were?

I think it's okay to ask when you started your journey, they need that sort of information. To phrase it as 'when do you normally leave the house' does sound a bit dodgy, but it might just have been sloppy scripting on the part of whoever designed the questionnaire.