If you'd like to hide the "Securely Processed By Paywhirl" badge from your widget, simply go into your widget settings and select "No" for "Show Paywhirl Badge on Widget?".
NOTE: THIS IS A CLASSIC SUPPORT ARTICLE FOR THE v1 SYSTEM. THIS SETTING IS LOCATED UNDER, MAIN MENU > ACCOUNT SETTINGS > MY ACCOUNT > SHOW BADGE ON THE NEW v2 SYSTEM.