I am just making a stab in the dark because I am not using Mint currently.
Is it the top panel or below the top panel (the window titlebar). Can you
tell us which Mint desktop environment (GNOME Shell, MGSE, Cinnamon, etc)?
Mint used to be a straightforward distro but it has gotten complicated by
offering too many desktop choices, IMO. When you say it is green, is it
themed green or is it a solid unsightly green bar? Does it appear with
every application or just FF?

If it has a top panel and a side launcher (called Dash) it is GNOME shell.

This may help describing it if it is GNOME shell:
https://live.gnome.org/GnomeShell/Terminology
Cinnamon has a bottom panel like this: http://cinnamon.linuxmint.com/
MGSE looks like this:
www.linuxmint.com/.../lisa_light.png

Assuming it is a driver issue and not a theme: This is just a GeForce card
and it is well supported with drivers. If this was my problem then I would
start troubleshooting by looking for another driver. Click on applications
at the top left and Type Additional Drivers in the search box on the top
right. When the application opens it should show if there is a recommended
new driver. Install it and re-boot. If it does not work for some reason you
can go back to the old one the same way or try a different one. Do not
install a driver outside of these ones unless you are desperate and know
what you are doing.

If it is just theme issue then go to Gnome-look.org and download a new
theme more to your liking. You can manage themes easily by installing the
GNOME Tweak tool.
www.techdrivein.com/.../...manage-gnome-shell.html