Hi,
To swipe texts up and dismiss them (like notifications or message previews), you usually just need to:
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On the notification panel: Swipe the message notification upwards to clear it.
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In the Messages app: Swipe left or right on a conversation to delete/archive (depending on your settings).
If you want to swipe up specifically to dismiss notifications or clear messages, make sure your phone’s gestures or notification settings haven’t been customized differently.