If a fictional character in a movie or TV show has pierced ears, is it really both the character and the actor who have pierced ears, or merely the actor?
If, for example, a character does not wear earrings but a close up of her ear when she uses her super hearing shows pierced ears, the character may be someone with pierced ears who is not wearing earrings at the moment, or the character might not have pierced ears but happens to be portrayed by an actor who does have pierced ears.
In the latter case the pierced ears of the actor would not be any more important than a butterfly which fluttered by during an outdoors scene, and would simply be a minor unintended aspect of filming the show or movie.
Since the earrings were actually shown in the scene, there are several possibilities.
1) The character and the actor are both wearing clip on earrings in the scene and don't have pierced ears.
2) The actor wore clip on earrings to portray a character with earrings in her pierced ears.
3) The actor wore earrings in her pierced ears to portray a character with clip on earrings in her non pierced ears.
4) The character and the actor are both wearing earrings in the scene and have pierced ears.
5) The character has non pierced ears and was not supposed to be wearing earrings in the scene but nobody noticed that the actor was wearing earrings.
6) Nobody in the production thought about whether the character has pierced ears or not.
Thus it is uncertain whether Supergirl is supposed to have pierced ears.
If it is determined that Supergirl is supposed to have pierced ears, fans may select the e theory which seems best to them to explain how they were pierced, until a canonical explanation is given.
For example, if Supergirl met Superman in the first episode and spent some time with him off screen, she might have asked him to use his heat vision to vaporize small holes in her ears, in addition to other suggested methods.