You can not delete individual messages on Langmate.
However, you can delete entire discussions if you Unfriend someone.
When you Unfriend someone, you will also disappear from their friend and Match lists, and they will disappear from yours.
To Unfriend someone, go to the Message section > open your Match discussion > tap the menu icon in the top right corner > Tap Unfriend.
You can also Unfriend a Match from the Friends list. Go to the Message section > scroll your Friend list until you find your Match > tap the menu icon in the top right corner > Tap Unfriend.
Note: Unfriend is a permanent action and can not be canceled.