Where is my card stored?
In this browser only — nothing is sent anywhere. Clearing your cache or site data resets it; "Shuffle new card" and "Reset marks" both work the same way, changing what's saved on this device.
What if I don't want to say anything back when I hear one of these lines?
Staying quiet is a legitimate response, not an incomplete one — "not taking the bait" is explicitly the skill this page points to, not just naming the pattern out loud. Silence, a subject change, or just marking your card internally all count.