urgent : ear piercing hole with purple marker inside, pls help. Will my daughter need surgery?

This marker will go away just give it a few weeks, i would not worry she will not need surgery for this.

The ink used to mark your daughter's earlobes will go away, don't be concerned. It is called gentian violet, and is also used (like betadine) on wounds that need healing. It will fade, don't worry.

Tattooing from marker is possible, though it would be unlikely. You can try to irrigate with isopropyl alcohol and or soak with gauze if you're concerned but it would still be rare to happen.