Are you referring to the Instagram icons and links on the top of the right sidebar of your homepage?
It appears that the StudioPress “Magazine Pro” theme comes with the “Simple Social Icons” plugin. This plugin adds a widget to your site, I’m guessing you would just need to access the backend area of your site and navigate to Appearance > Widgets, open the “Simple Social Icons” and make edits/remove Instagram and click “Save.”
You must have added your Instagram username to Customizer or theme options, you could probably find that and remove it, which would probably remove the icon and link from your homepage, too.
