mailgun - which key am I supposed to use?

I've set up mailgun and I notice that I can receive emails whether I have the public or private key setup

it works in both cases. Actually I suppose you can receive emails without even setting up the key. The key is only for replying?

Is it the public or private key we're supposed to use?

Review the project's Mailgun setup and configuration guidance, then verify how the public and private keys relate to receiving and replying. Done means the documentation clearly states whether a key is needed for incoming mail and identifies the correct key for replies.

Written by the indexing model from the issue text.