I had the same problem too, but I figured it out!
Here's what I did to change the background:
1. Click Plugins
2. Click Editor
3. In the upper right hand corner, click the lookin box saying "select plugin to edit:"
4. Select Jetpack and click select button
5. On the right hand side find and click : jetpack/modules/widgets.php
6. On the right hand side find and click : jetpack/modules/widgets/facebook-likebox.php
7. Put your cursor at the top (1st line) and count down 58 lines by hitting your down arrow key on your key board.
8. On the 58th line you should see:
(line 57:) $like_args['header'] = (bool) $like_args['header'] ? 'true' : 'false';
(line 58:) $like_bg_colour = ( 'dark' == $like_args['colorscheme'] ) ? '#000' : '#fff';
You can change both #000 and #fff to the hex code color that you want so that no matter if you've chosen dark or light, the background color will be the color of your choosing.
Let me know if that helped any :D