Currently you can only reset your progress in a level or a course via the Memrise website (you cannot do this within the app).
After logging in with your username and password, visit the main page of the course you would like to restart, and click Options under your progress bar. From the drop-down menu you will be able to select Restart. Quitting or restarting a course will not deduct points from your overall score.
To restart a level, simply click a level, and select Options>Restart.
Please note: after you've restarted a level or a course, you may have to log out and in again on the app to see the changes appear.
What is the difference between quitting and restarting a course?
Quitting a course will not erase your learning history, you can always go back to the course and continue learning where you left off. Quitting only means it will be taken off your course list in the dashboard.
Restarting a course will effectively wipe all learning history in that course. This means if you ever want to learn that course again, you will have to start from scratch.
Both restarting and quitting courses will not erase any of your points.