Adding a check valve reduces the time it takes to fill the tank, as it eliminates the volume to be refilled in the line up to the coffee maker. It's asynchronous, so the time itself doesn't matter, but it will prevent the motor from wearing out as quickly as it would have, and saves energy, etc.
Here is the top end of the tube. It is threaded through a polyethylene tube of larger diameter, which has been bent with a little heat.
This part can just hook over the side of the tank, which conveniently already had a relief.
The cover fits completely without modification.