@Jacie
Sometimes the problem is the fact that they laser cut the labels. This makes the edges very sharp or " scratchy ".
If this is the case, just trim the pointy edges. The other posters who have mentioned tape, that may fix the issue of not laying flat. For me, I would just cut close to the upper stitching and remove most of the hanging tag. ( My iron is being " preserved " for posterity, LOL )
HTH
We make a living by what we get. We make a life by what we give.
Sir Winston Churchill