How can I find out if someone deleted a Messenger message?

This question is unclear. Do you want to know if someone deleted a messenger message from your account? Or do you want to know if someone deleted a messenger message from their own account after you sent the message to them? Either way, the answer is that you cannot know.

Unless you were trusting enough to give someone else access to your account, you are the only one who can delete messenger messages from your own account. A device has no way to tell the difference between you and, another person who may have logged into your account pretending to be you.