When I "Empty the Pushed folder" or remove a pushed item, does it delete the copy in my task app?

No. Emptying the Pushed folder, or removing an individual pushed item, removes those to-dos from this app and your Supernote device — but they stay in your connected task app (Todoist, Apple Reminders, or Google Tasks). The confirmation message spells this out (e.g. "They stay in Todoist"). The push is a hand-off: once a task is in your other app, this app won't reach back in to delete it.

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