This luggage has logged alot of travel miles and so has that little red strip of fabric. Many years ago, when I was flying alot, I noticed that everyone had a piece of black rolling luggage that looked almost exactly like mine. When I got to the baggage claim carousel, I could never really tell if the bag was mine until I was right on top of it, until one day, I tied this little strip of red fabric (that was given to me on a gift at work) to the handle before a trip. From then on, it was always easy to spot my piece of luggage well before it got to me, and it was also easy for others to see that this was not their bag.
You could use a piece of ribbon or even a piece of colored duct tape in this same way to make your bag easy to identify for you and less likely to be mistakenly picked up by someone else.