It looks like the bar is done using Custom CSS rules (see below in yellow highlight).
These are in the theme Global Custom CSS Rule box, just change or delete the ones you do not want
/* Custom CSS rules for Ajax Subtheme */
.page-title{border-bottom: 2px solid #07D900;} /* add a bottom line to page titles */
#container .post-title{border-bottom: 2px solid #07D900;} /* same for post titles */
h3.widget-title{border-bottom: 2px solid #07D900;} /* matching for widget titles */