Yes, there should be a dedicated return that goes back to the cold
water inlet of the water heater . Put a check valve in the return line
so the water can't go the wrong way when the pump is off. Use a
stainless steel or bronze or hi temp plastic pump. I see a lot of
people use iron body pumps to save money, they die quickly & put rust
in the water. you can also return to a tee installed at the drain valve
on the water heater.
Easier to do with a crawlspace or basement than with a slab.
Sonetimes you have to go back into the cold line under the sink, but
that can cause problems, like putting hot water into the toilet &
cracking the toilet tank due to water temperature shocking the tank.



Stretch.