The endoscopy procedure itself will have no effect on a fertilized egg. However, anesthetic medications are generally used during endoscopy to provide comfort, and it's possible that these medications might have some effect on the egg.
We don't really know much about what might affect a developing egg. If a medication had some effect, it's likely that it would cause a miscarriage. We don't think that most medications used during endoscopy would cause a miscarriage or have any other effect on a fertilized egg, but there is no way to be certain about this.
If you're not sure if you're pregnant or not, it might be safer to have the endoscopy after a period and prior to ovulation.