If the felt is green, it is not typical to put felt on the bottom of a paperweight at the factory level. The felt was probably affixed by a dealer or a previous collector.
However, if the felt is navy blue, the paperweight is probably made by Antica Murrina Veneziana, which does put this color felt on its pieces. However, there should be a silver sticker with the full name Antica Murrina Veneziana on it. But, of course, the sticker can always be removed.