Your data
Out of the box, everything stays on the device — 100% local, nothing to sign up for, nothing sent anywhere. Want a grid on your other devices? Publish it into your own iCloud account and join it from the others. Want somebody else to see it? Share it, and that goes through iCloud too. Nothing leaves until you say, and when it does it travels only through Apple’s own sync services — Dash has no server of its own.
Every device that has joined a grid can log to it. Tap a glass of water on the iPad and tap a walk on the phone — offline, in either order — and the next time the two sync, the day is merged entry by entry: nothing is lost and nothing is counted twice. Deletions sync the same way, so a device that was switched off when you cleared a box won't bring it back.

A grid's Share pane. In iCloud, on the Watch, shared with nobody yet.

The grids list. The cloud beside a grid says it's published; grids waiting for you from another device appear here to join.
"Stop sharing on this device" and "remove from iCloud" are different sentences, and Dash keeps them apart: the first leaves the grid on the device and the copy in iCloud alone; the second takes the shared copy away from every device but deletes nothing anyone already has.