I can't reproduce your exact set-up, but I can reproduce the background appearing behind certain icons.
It appears that the issue lies with the choice of GTK theme.
While I don't have ThinIce installed, I have others. I used Lubuntu's Customize Look and Feel application to change GTK themes.
In the animation below, you can see
- a white background with "Materia-light"
- a dark background with "Materia" and
- no background with "Lubuntu-default"
In addition to Lubuntu-dark, other suitable themes include Greybird and Numix which you can install using
sudo apt install shimmer-themes.
I prefer to use themes in the repositories because they're more likely to be suitable for the GTK version of the OS. If you want to use themes from elsewhere, ensure they're recent and support your GTK version (which you can check using
apt policy libgtk-3.0.)
ThinIce and some other themes in
/usr/share/themes contain only a gtk-2.0 folder while some other themes such as Emacs and Default contain a gtk-3.0 folder as well but aren't suitable for general use.