You don't say what age the child is.
For an older child - 6+ I would leave it alone. The kid was old enough to think about it and the SIL thought it was a treat for both of you.
For a younger child- baby+ I would be upset. She made a parenting decision that will/can affect the child's well being without consulting you. It is not her child so it is not her decision to make.
Next time something like that comes up I would make a point of not doing it with SIL in tow. Or I would make a point of saying it is something to think about and that you want to talk to dd more and this is just a discussion--not action at that time. Be real clear so there is no question of what you want or desire to see happen with your children.
btw I am guess this gal has no kids of her own. I can't imagine a fellow mother would do this. She probably does not realize the extent of doing something like this with someone else's child, so you have to cut her a little slack as the aunt that wanted to be fun and helpful. ;-)
I have to say am shocked that they would do it without parental consent. It was my understanding that any piercing, cutting, invasive procedure in the state of Texas had to have a signed parental consent and parent present. I know my dd had to when we pierced her ears.
ps. don't forget to clean them daily and turn the earrings a little to prevent growth around them making it hurt when you do change them.