When you tap on the Tailor of Fortune, Lost and Found, the Carpenter of Chance and the Recycler, you can see which items you have already received in the top left corner of your screen. The icon looks like a small blue box. If you open it, you will see your collection.
Once you’ve acquired all of the Tailor of Fortune items in a row (a full set), you’ll get a bonus reward that you can see on the right hand side of that specific row. You can switch tabs to check your outfit collections collected from the Lost and Found, the Carpenter of Chance and the Recycler as well - just tap on their icon tabs.