If you wish, you can delete the whole conversation (not the individual messages) made with another player (he will continue to have it).
To delete private messages, open the messages with the appropriate button (indicated by the red arrow in the image below):

then he must click on the red X of the conversation he wants to delete (as indicated by the yellow arrow in the image below)

The following question will appear

just click on Yes (the button indicated by the yellow arrow in the previous image) and the conversation will be deleted forever from your device.