Frankly, any MP who takes offence at such trivia does not have the mettle needed for political office.
If this Eagle woman was ever given a position of authority, she would be told (in the usual way), that she was ...
incompetent, betraying the public, irresponsible, deceitful, should resign, etc
If she feels so hurt by being called "dear" ... she would never cope with that.
Perhaps she should resign from being an MP.