There has been something going on over the last few months with the Promoted Sites on SharePoint Online. If a user logs into there MySite by clicking the "Sites" button on the Top Navigation, they will see duplicate Promoted sites.
To fix this, its actually quite easy. You need to login to the SharePoint Admin Center (Admin Dropdown – Choose SharePoint). Once your in the SharePoint Admin center, if you click user profiles on the left quick launch and then choose Manage Promoted Sites on the main page.
Once you click on Manage Promote sites, here you will see that the same links are duplicated. Now, even know i blurred out the first part, you can see that they are the same. All you need to do is put a check in the box just before the URL and then click where it says Delete Link. Now, one thing i did notice is that the URL’s had the first two letters in CAPS. So, I am not sure what is going on at Microsoft but lets hope they get this fixed.
Now, on a side note, while you are in here. This is a great place for you to add new links so that when all your users sign into there mysite, they see all the promoted links you want them to. Maybe you have other site collections, or some off-site websites you want to add. You can do that right here just by clicking where it says "New Link"