a song with a green arrow in the right hand corner
A green arrow, on corner like a piece of paper you can peal away?
That arrow marks songs stored in iCloud. To be able to open them, you need to connect to the internet. Then GarageBand can download and update them. If you see the message "the song is damaged or in a format GarageBand cannot read", then you need to save the song again to iCloud on the device where you created the song. I see this message, when I try to edit an GarageBand for iPad song with GarageBand on my Mac and try tosave it back.