The oil tank and filter is fed into normally a charge pump to push oil into the main belt driven pump. Which is then sent to the wheel motor in one direction or the other depending on direction of travel of the mower. There is a certain amount of oil that is lost due to internal leakage of the pump and wheel motor. That leakage is sent back into the oil tank via low pressure lines, where it is then filtered and then sent back to the main pump to make up for system lose.
The oil that is returned from the wheel motor is recirculated through the main pump and then back to the wheel motor, basically acting as a closed loop system. So the only oil in the system that get filtered is the oil from internal system leakage. So the debris from a failing wheel motor goes back and forth between the wheel motor and the pump which is the reason why a failing wheel motor will damage a pump.