The Simon And Garfunkel legend and his singing spouse hinted at a reconciliation by singing about their love on a new track, 'Like to Get to Know You', which was shared on Edie's SoundCloud page.
The married musicians croon in unison: ''I wouldn't trade places with anyone, none of them, 'cos I'd like to get to know you again.''
The united front comes after police officers arrested the couple at their Connecticut home on Saturday (26.04.14) for disorderly conduct.
In court on Monday, Paul, 72, and Edie, 48, insisted their dispute was a minor disagreement and they have never lashed out at each other like that before.
Edie said in her statement: ''I got my feelings hurt and I picked a fight with my husband. The police called it disorderly. Thank god it's orderly now.''
The folk singer - who has three children, Adrian, Lulu and Gabriel, with her husband of 22 years - added that Paul was ''no threat to her at all''.
In his statement, Paul echoed his wife's sentiments, saying: ''We had an argument, which is atypical of us. Neither of us has any fear, or any reason to be threatened - we love each other.''
The pair left Connecticut's Norwalk Superior Court hand-in-hand after appearing before a judge.
They are due in court again on May 16.
There are currently five separate teams working on 'Game of Thrones' projects at HBO.
She's a big fan of the band and this week she got to perform with them.