When you copy a message link into chat, Fletcher will post the full message as a quote. Sometimes this is too long to fit in one message (speculation: because quoting a message takes more characters than writing it without quotes), and so splits it into two messages. Fletcher does a :deletethis: emoji at the bottom of the message (bottom of the second message, in the case of two messages). When you click that message, in the one-message case, Fletcher will correctly delete that message. In the two-message case, Fletcher deletes only the second (overflow) message.
Example: https://discord.com/channels/298182830582923264/298246693508481024/1274917893620105379