Water Heaters - Grunfos hot water recirculator

I purchased and installed a recirculator on my existing system. This is the one where you install a line between the hot/cold lines at the sink furthest from the tank. It works fine except that the cold water side is now heated, too warm for drinking. I would like to tap into the hot line at the furthest sink and run it back to the tank. I don't know which side of the shutoff valve on the tank inlet to tap into. Also do I need to put in a check valve of some sort? Thank you for whatever help anyone can give. Ken

Do you really mean you installed a crossover
line or did you buy and install the system that has a plastic thermostatic valve that installs at a faucet with extra supply lines?

Big diff between the two as how you wrote your question with a cross over line wouldn't work