You can’t stop the Wyze app from storing notification videos on your phone. If you want to view a notification, the app downloads it to your phone, first. This is better for people with limited data plans, because if you want to view the notification video again, the app doesn’t have to download it again. To get rid of the videos from your phone permanently, you have to clear the cache through, “Account”, and then the “App settings” page.
The functionality of the gallery app on Android is often misunderstood. It searches the entire phone for photo and video media. So, they’re not “in the gallery app”, they’re somewhere in a folder on the phone where the gallery app finds them. A common misconception is that media files are duplicated, but they aren’t, it just appears that way because the gallery app finds them where the other apps store them. There’s sometimes a way in the gallery app’s settings to “hide” folders, but the media is STILL there on the phone, just not shown in the gallery. Another way to “hide” the media, is to place a “.nomedia” file in the folder.
Changes in more recent versions of the app seem to be automatically clearing event videos more than it used to. If that is not your experience, I would recommend contacting support.