If your partner can see your events or to-dos but you can't, they're saved. They're just hidden on your phone.
At the top of the calendar (day and month view) and the To-dos screen there's a row of three coloured buttons: Me, your partner's name, and Us. Each one has a tick when it's switched on.
Me shows your own entries
Your partner's name shows their entries
Us shows the entries you share
A button without a tick hides those entries on your phone only. Nothing is deleted, and your partner still sees everything.
To show them again, tap the button so it has a tick.
Android: Cupla remembers your choice until you tap the button again, even after closing the app, restarting your phone or logging out.
iPhone: all three buttons switch back on every time you fully close and reopen Cupla.