how can I close this dropdown terminal?

This looks like one of either tilda, guake, or KDE's guake fork yakuake. Tilda's default keybinding is the tilde key (~) or sometimes F12. Both guake and yakuake bind to F12 by default. Try pressing one of those keys and see if the terminal disappears.

You can use apt-cache to quickly see if one or more of these emulators are installed:

apt-cache policy tilda guake yakuake | grep Installed -B 1

From there you can either uninstall the offending application or change its keybinding.

My bet is on tilda, as it actually ships default in Ubuntu MATE 15.04.

You can kill any GUI program with xkill command and selecting the appropriate window. Your bigger issue is figuring out what drop down terminal you've installed. There is yakuake and guake, but if you want more precise answer , try this:

1. Find out that shell's PID with echo $$.

2. Use pstree -p | less to list all processes with their pids in brackets.

3. Use / and type in PID of that process

Or in a single command:

 pstree -p | grep -C 10 --color $(echo $$)