Did they just remove the Background settings for Terminal?

About 10 minutes ago I set up my basic Terminal app to be semi-transparent and was really happy with the result. Now, some updates ran and the whole "Background" tab is gone from Terminal settings. Was this option removed? If yes, why? Why would anyone do that?

I'm running gnome-terminal 3.10.2 from the Gnome3 ppa.

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.

The transparency feature was indeed removed from the recent versions of the Gnome Terminal. As noted in the other answers, you could use Devil's Pie program to make any window transparent (and more).

Here's how to set this up in Devils Pie 2 (it uses Lua, so scripts for the original Devil's Pie are not compatible with this version). I'm using Debian Buster, but it should work the same in Ubuntu.

1. Install Devil's Pie 2 right from the official repo: sudo apt install devilspie2.

2. Create the ~/.config/devilspie2/gnome-terminal.lua with the following contents:

   if (get_window_name()=="Terminal") then
     set_window_opacity(0.9);
   end
   

3. Create the ~/.config/autostart/devilspie.desktop file, which something like this inside:

   [Desktop Entry]
   Name="devilspie"
   GenericName="devilspie"
   Comment="The Devil Spy 2 script"
   Exec=/usr/bin/devilspie2
   Terminal=false
   Type=Application
   X-Gnome-Autostart=true
   

4. Logout and login again or just reboot. All set!

In the Lua script, you could tweak the set_window_opacity(0.9); setting, 0.9 means that the window will be 90% opaque.

You can also add any other command which Devil's Pie 2 supports. The list could be found here.