Sorry my bad, seems like you designed your survey project with pages as Form style. Try using the Default - single page as shown in the image below, which should solve your issue.
My point for your second argument was that if you put a skip at the group level, you should be able to skip the entire section, which will take the icon away with it. Else, if you try to keep the skip in the individual question level, your group will be seen despite the individual questions being skipped.
I hope this helps you.
