The transmission cooler is built into the radiator from the factory. If the previous owner stopped using it and installed a different cooler, he probably didn't touch the lines that run to the tranny and just extended them to the cooler he installed on the front of the car.
I kept my stock tranny cooler in place AND added a cooler as well.
If he didn't remove it, you'll also notice that your engine oil cooler runs to tjhe radiator as well (if it has stock tanks).
What kind of radiator do you have?