How can you get rid of the messages that says someone kept an audio message from you… if you and the other person deleted all the audio messages y’all sent.

Greetings, Lauraengleton.

Welcome to the Apple Support Communities. It’s understandable that you’d want to know how to get rid of the notification that an audio message was saved. 

What happens if you delete the conversation?

“Delete a conversation

1. In the Messages list, swipe left on the conversation.
2. Tap Delete.” Delete messages on iPhone 

Do the notifications appear when you start a new conversation?

We hope this helps! Thanks for being a part of the community.

Sincerely.