Miss Godinez-Avila slipped from her harness 30 seconds into the flight. She clung to Orders' body for a short time and pulled his shoe off but fell when she couldn't hold on any longer.
After his court appearance, Orders told reporters he wished he could relive the day and have it turn out differently.
"I will be left with the events constantly going through my mind, and that I will have to endure forever. Please believe me when I say I am sincerely and deeply sorry."
Orders apologised to the victim's family for his "panicked action" -which he blamed on "overwhelming stress" that included having his 12-year-old daughter waiting where the flight was supposed to land.
He said he now realised his actions had caused further pain for Miss Godinez-Avila's family and brought negative attention to the hang-gliding industry that had been his "passion" for nearly 20 years.
"I have concluded that I cannot and will not return to hang gliding," he said.
His lawyer Lori Stevens told Canadian media he held expired New Zealand, Australian and British passports.
A Foreign Affairs spokeswoman last night said they were not aware of the case and consular assistance was not being provided.
Orders will return to court on June 18.