"Menace" ㅡ"Suck up"
They were having a quarrel. I don't get the phrasal verb here. Does it mean "flatter me"? But it doesn't make much sense to me.

Question

Answer

1)It is derogatory.  To call someone a "suck up" or to "suck up" to a person is to be nice to that person for personal gain.  
2) To "suck it up" means to quit complaining and finish the task.

Answer

Not sure why you put "menace" there so I won't answer that.

To be a "suck up" is to do something for someone just because you want them to like you.

Example:  Wow, look at how hard Roy is working today.  He sure is a suck up. 
                 (meaning he sure wants the boss to like him) 
                    It's not nice to say - it's said when you are saying someone isn't 
                    giving out of honestly...they are giving because they want something 
                    from the person they are helping.