Is one allowed to remove on Shabbos a dry cleaner tag or price tag that is fixed onto an article of clothing?
From your question it seems that you are asking about removing a dry cleaner or price tag that is stapled to the clothing. If it is attached to the clothing in a place that is not noticeable and it might remain there for a while, then it should not be removed on shabbos. It is permitted to walk outside with it on shabbos because it would be considered botil to the garment. However if it is a place that it is noticeable and therefore meant to be removed right away, then it may not be carried outside on shabbos, and it should be removed before shabbos. If it was not removed before shabbos there are two problems with removing it on shabbos, korayah, and muktza. If possible don’t remove it. However if the garment is really needed, then there are opinions that one may rely on to remove it on shabbos, however it should be done in private, and if possible it should be removed with a shinui.
Chut Shani 1 pg. 136, Shmiras Shabos Khil choso5-85, Orchos Shabbos 11-13 and ftnt. 18, Shearim Mitzuyanim B’halacha 60 Kuntris Acharon 45.