If you want to delete messages from both sides of an Imessage conversation, there are a few different ways to go about it. The first way is to open the conversation on your iPhone and tap on the three lines in the top left corner. Then, tap on the “Message” button in the bottom right corner and select “Delete Message.” If you’re using an Android phone, open the conversation and tap on the three lines in the top left corner. Then, tap on “Message” in the bottom right corner and select “Delete Message.” Once you’ve selected “Delete Message,” you’ll be asked if you want to delete all of your messages or just this specific conversation. If you want to delete all of your messages, just press OK. If you only want to delete this specific conversation, press Cancel and then select “Delete Conversation.” ..