On the following link of my site, I have a featured news item using the K2 component. Since my site is in Spanish, I would like to remove or change the small image with the red band that says "Featured".
Just for your information, I was playing with this myself last week and selecting the hide featured notice next to title turns off the "Featured" text to the right of the title but then activates the "featured" icon in the upper right corner of the article. So by default either you show the "Featured" text or the "Featured" icon.
There are three ways I can think of to not show the icon,
1 as mentioned above is to make the icon a transparent PNG,
2 and probably the most efficient is to go to the K2 CSS around line 127 look for this code " background: url("../images/system/featuredItem.png") no-repeat 100% 0; " and change it to this " background: none; " or
3 you could go to the template and completly remove the code for the featured icon but only if you know what you are doing. I would recommend the 2nd choice. Hope this helps.