It's an interesting phenomenon. I listened to several recordings by Melanie. In all of them, Melanie sang "Look what they've done with my song." On Spotify, some of the Melanie recordings are listed as "What Have They Done To My Song," and some as "Look What They've Done To My Song." I listened to a number of them and none of them sang it as "What have they done..." Go figure.

The Harry Fox Agency, which handles licensing for this and most other songs in the US, covers all the bases. It identifies the song as:

WHAT HAVE THEY DONE TO MY SONG, MA, A/K/A LOOK WHAT THEY'VE DONE TO MY SONG, A/K/A LOOK WHAT THEY'VE DONE TO MY SONG, MA

Interestingly, it identifies the songwriter as Melaine Safka (sic), and the singer as Melanie. Harry Fox reminded me that "Melaine Safka" also wrote "The Nickel Song" and "Brand New Key."

-Joe-