I see, but I'm not sure what the solution is. To get to the EXP Progress screen, you have to click on the "Save & Continue" button. With this saving, it is implied that you won't lose progress if you pass that point.
A through explaination for how resetting works is given in the Settings Menu. There isn't room to do the same here.
If I were to replace the reset icon with text like "Reset Run" or "Try Again", it would lead to the same confusion in your conclusion. A "Play" button would be out of place. What do you propose I show instead of the reset icon?