I just wanted to add that I had this problem on an iPhone 6, changed the password, and it did not work - the message forwarding still had the list of the old devices. In addition, even though all those devices had message forwarding turned OFF, one of those devices was still receiving forwarded messages.
The reason it didn't work for me is because I was not aware of ALL the things that must be turned off to disassociate one device from the rest of your devices. To disassociate a device, you must change all of the following IDs (at minimum, no idea whether there are more):
(1) AppleID in Settings -> iTunes & App Store
(2) AppleID in Settings -> iCloud
(3) AppleID in Settings -> Messages -> Send & Receive
(4) AppleID in Settings -> FaceTime
I did not realize the ID must also be manually changed in Messages and FaceTime, I thought the iTunes and iCloud would be enough.
I also note that the Forwarding function is clearly BROKEN, because even though forwarding was turned off on my iPhone another device was still receiving the forwards.