You can isolate the image and disable it using CSS but first you need to know the css path for that image.
For the fronpage it is this...
#page-site-index .enrolmenticons {visibility: hidden;}
Depending on your theme, you can either add the CSS to your theme's Custom Settings page, or add that CSS rule directly into yourtheme/style/core.css or whatever name your CSS stylesheet is called. If you add the CSS to the stylesheet you need to add it at the very bottom of that file.
Before you do any of this it is best enableing Theme Designer Mode from Site Administratiion > Appearance > themes > Theme settings as this will allow the changes to be seen. You will also need to refresh your browser window to using Ctrl + F5 which forces the page to reload.
Mary