I only know such a screen issue from defective graphic card chips or when the graphic card has driver issues. Maybe it's just a software fault, maybe there's something wrong with the internal graphic chip / GPU or just a loose cable from the display. That's only speculation as I don't know on which system the Encore is based. Some say Linux, some say Android... and as always, there's sadly no info from B&O.
The Encore is based on a Freescale MPC512x (ppc architecture with embedded graphic unit) as far as I remember. It's running an old wind-river Linux distribution for embedded systems. Bootloader is u-boot with tftp support, it has two rootFS's with bank switching on NAND and an replaceable microSD card where all user data (databases, etc.) gets stored. SSH server is permanently running on port 909 but started in "not-forking" mode (which makes it invisible to standard port scanners).
I'm not sure whether a loose cable can only affect the background color. In the picture it looks like black and white are working normal on the "arrow" graphic. If it's a hardware fault I would say it's the LCD display (or the embedded display controller) itself.
If the author has the latest software installed he can go into "service menu" and enter "service mode". This should show a grey background labeled with a large "service mode" text and the IP address. If it's still green, I have my doubts that its a software issue.