Im not sure what to do about this. The full message stores the message in full so the version that is emailed out, for example, is intact. However messaging UI uses the "smallmessage" version which has had strip_tags() called on it when the message was sent between users. This is to stop users from injecting potentially harmful html.
What this means in practice is that this
this is my <p>message</p>
will result in a message that says "this is my message". The p tags are removed but not the text within them.
However in the case of this...
Please contact our support <firstname.lastname@example.org>
removal of what looks like a html tag results in part of the message being stripped out.