For most of the 2000s, Rolex affixed green holographic stickers to the back of a watch case in order to confirm authenticity. The problem was, the stickers were very easy to counterfeit. That made using them for the sake of authenticity uncertain. Rolex moved away from the original green holographic caseback sticker and replaced it. The new sticker was transparent with a small half-moon shape on it. This sticker was a bit harder to imitate.
If you buy a new Rolex today, the new version of the sticker is what you’ll see. If, on the other hand, a Rolex comes back from servicing, the sicker on the case will be transparent with a single red line. The red stripe caseback sticker is placed there to indicate the movement was closed back up after its service.
For the most part, unless you’re buying a new, unworn Rolex or one advertised as just back from servicing, you don’t need to worry about the sticker.
***FOLLOW UP*** Is a caseback sticker part of a full set? The truth is most people will neither save the sticker nor let it remain on the caseback before wearing the watch. Some people save the sticker, keeping it with the box and other paperwork. There are some sticklers who want every single item, no matter how small, that came with a watch, and for them, the sticker is part of a full set. For most buyers, it isn’t.