The maps API key for your eDirectory site is meant to be public.
- Log in to the Google Cloud Console and review the API and billing activity on your account, ensuring the usage is in line with what you expected.
- Add API key restrictions to your API key.
Authenticate using API keys | Authentication | Google Cloud
Restrict your "eDirectory project" API key to only be used by that project (following the steps on the link above).
Note: you may need to generate another key for your maps to be used exclusively by myedirectorysite.com
For further info on Google Maps on eDirectory:
How to activate Google Maps : eDirectory - Support Center
Note: step #3 instructs on how to restrict the API key