My ice maker has a gravity drain that it says to connect to the sink drain. All works well except if I run the faucet for a while eventually water will back up into the ice maker. I believe the issue is that the drain connects to a pump that pumps the water up into my sewage line, and my guess is when the pump kicks on it may back up the water in the pipe...but I am not sure if that's actually the issue or not. Picture of the setup attached, the grey line is what connects to the ice maker, the pipe closest to the wall goes up to a studor vent. Any ideas for changes I can make to stop this from happening? Is there a one way valve I can get for this or a different position for the grey line that would help?
Also side note, I plan to add a garbage disposal to the sink, is that a bad idea with the pump?