The 54-year-old star - who was the lead guitarist of the rock band Bon Jovi until he dropped out of the band's world tour in April for undisclosed personal reasons - includes words on the song which appear to refer to his spat with the singer.
The song features the lyrics: ''What do you want me to say / I'll tell you anything you wanna know / You want to know about disappointment, baby I haven't watched that show.
''What do you want me to say / I gave it everything I could give / But everything just wasn't enough so I just let live and let live.''
Richie gave a knowing wink to fans about the lyrics as he announced the song, tweeting: ''Since everybody was diggin' stuff figured I'd lay something new on ya. And the lyric is pretty timely.... (sic)''
Despite Jon's previous suggestions Richie was having problems in his life, the guitarist's lyrics claim he is happy with himself.
He sings: ''In spite of it all, in all that you see / if I die tomorrow, I'll come back as me / Not Elvis, or God not Frankie not Dean / If I die tomorrow I'll come back as me.''
Corgan took to Instagram to confirm rumours of new Pumpkins material, saying the first songs could arrive as early as May.