My proposal to achieve the given task will be storing the master password on the app. Hence when user tries to delete the special contact, i.e at the top right corner, then prompt the user the user for password. If the password entered is correct that matches with the one in the app,then the operation should be completed. otherwise not.
I thought this is the best solution, because for every app installed there will be a master password stored on the app.
(This may be extra feature that can be added to the app)
To retrieve the forgot password, we can send OTP if the user's contact details are with us(I am guessing we are maintain user contact details if not, the only option may be reinstall the app).