Unfortunately, due to the way Android OS operates, 3rd party dialers like drupe cannot interfere with the device's infrastructure, i.e., the stock dialer and contact manager apps.
Therefore, the dialer will continue keeping the record of your missed calls and your call log, even while you are using drupe to keep track of your calls. Dismissing drupe's missed call bubble (by dragging it to the X at the bottom of the screen) will not dismiss it in the stock dialer accordingly, we simply can't do that (sorry... 😔).
If you are bothered by the notification count badge that appears on your stock dialer's icon, you could simply keep the dialer in the app drawer and replace its icon with the drupe dialer icon (drupe settings > Add drupe dialer to home screen), or turn off the BadgeProvider (Android settings > Apps > All > BadgeProvider > Disable).