Did they just remove the Background settings for Terminal?

Standard versions of Ubuntu use gnome-terminal 3.6.2. The background tab was removed in version 3.7. The ppa, as you saw, provides version 3.10.

You have a couple choices:

1. Purge the ppa, then run an update and an upgrade to restore the standard packages. The trade-off is that you will lose the other features of Gnome 3.10 that you may want.

2. Follow the instructions at How can I make the terminal transparent? to emulate the feature in 3.10 (quoted below):

   Since version 3.7 this option has been removed from the Preferences dialogue. You can however still get the same effect by setting the _NET_WM_WINDOW_OPACITY X property, for example with the Devil's Pie or Devil's Pie II tools. E.g., set up Devil's Pie to start automatically with the session, and create the file ~/.devilspie/gnome-terminal.ds with these contents:

(if
(matches (window_name) "gnome-terminal-window-*")
(opacity 90)
)

You can also use this shell script that however only works for existing terminal windows and not automatically for newly created ones.

Vivid 15.04 brings back the transparency option. (It's not part of mainstream gnome-terminal, but Ubuntu applies a patch to bring it back.)

On the other hand, background image support is gone for good.