I guess I first heard "Jenny's Gone and I Don't Care" on the 1964 Highwaymen recording on Homecoming: Recorded Live at Wesleyan University:

https://www.youtube.com/watch?v=IPHqBP9gvqU

JENNY'S GONE AND I DON'T CARE
(Mike Settle and Alan Ribbock)

1
[Verse 1]
Jenny went and ran away
Find a new girl any day
Jenny used to be my friend
Now, she's gone and I pretend

[Chorus]
Lots of girls in love with me
When she comes back she will see
Pretty girls are everywhere
Jenny's gone, and I don't care

[Verse 2]
Why did Jenny run away?
Found a new love so they say
Think she's still in love with me
Should I wait around to see?

[Chorus]
Lots of girls in love with me
When she comes back she will see
Pretty girls are ev'rywhere
Jenny's gone, and I don't care

[Verse 3]
When the rain begins to fall
Think I hear her faintly call
When the sun begins to shine
No, it's just a dream of mine

[Chorus]
Lots of girls in love with me
When she comes back she will see
Pretty girls are everywhere
Jenny's gone, and I don't care
Jenny's gone, and I don't care

Lyrics corrected from https://genius.com/The-highwaymen-folk-jennys-gone-and-i-dont-care-lyrics