Hello!

It seems you're using an older version of Messenger. In the latest version, the options to edit and delete talks are no longer available in the same way only Administration talk action is available for managing conversations. Additionally, there are options in Messenger->Settings that let users edit their own conversations and messages.

For your situation, you should:

1. Disable the Edit and Delete Talks membership actions.
2. Go to Studio > Messenger > Settings and enable the options that allow users to moderate their own talks and messages.