To make sure that you will not be caught for plagiarism, using AI you may undertake following steps:
1) Run the text through plagiarism checkers widely available on the internet.
2) Read through the text to be certain that there is no clear nonsense or AI-talk.
3) Fact check. AI is known to be making up fictional facts and weird mistakes.
4) Re-generate problematic places and/or finetune manually.
Follow the steps in ascending order, depending on how much you care.

Here is more detailed answer:
The authenticity verifier (teacher/professor in your case) will most likely use one of the plagiarism checkers available online. Depending on your language and country you may search for some of the most popular and check yourself. But since the mechanism of text generation in GPT-like models does not suppose basic copying and pasting, this test would be done more for self-comfort.
Your work presumably will be read by a human. Humans in general are good at spotting gibberish, some can tell rather easily if something was written by AI or not and academic workers have a tendency to verify facts. In addition the verifying person may be familiar with your writing style and become suspicious. Manually editing and rewriting are considered effective in such cases.
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