Welcome on your first post, and hope someone with one can help you. I have some general advice, but I don't own one of these.
The cables are analog composite cables, and because of their connector,mare also called RCA cables. Its actually got two video signals in there put together (composite), which is why other cables like component cables will produce better video. In older computers and some VCRs, you could tune the output, but thats not likely an option here.
If you search on Google for help, try using terms like composite, rca, or even 'av'. AV is not a very precise term, but its common shorthand for things like making a composite modification on older systems.
It could also be local interference or a bad connection. If you have another set of those cables lying around, try to swap them out to see if its the cable. Sometimes those cables have an issue by the plug end. You could even plug the red or white into the yellow jacks and see if its the yellow cable - it wont hurt anything. It could even be the soldering inside directly on the video jack.
Does it happen on many games, or just ones like the low res Gameboy games? One knock on the system is the quality of the emulation being used. http://atariage.com/forums/topic/253811-retro-bit-generations/
is an AtariAge forum thread on this device. I didn't wade in, as their threads can be very long, but thats a source of information too.
Hope someone can help you more - good luck.