There is no pop-up to indicate the added Closet Value.

If you're curious about the value of your closet, visit the single person icon at the bottom of the screen, tap profile, and you can see the total value of your closet as well as the value for the current season.

Since these garment prizes can be from any season, keep an eye on your total value to see your added Closet Value climb. Earn enough Closet Value can help you level up even faster, so keep collecting those prizes!