I don't even notice it.
I had the transponder mounted in the center of the windshield just under the mirror mount on my previous car, but with the windshield box on the Renegade that's a no-go.
The annoying thing I always found with mounting them on the glass is that, from the outside, you have a view of the sticky side of the velcro mounting strips.
That being said, I initially did install it on the passenger side like you mentioned, but the Velcro I used had adhesive that wasn't up to the task, and after a day in the summer sun I came back to sticky residue on the windshield and the transponder on the floor.
For this mounting, I used the 3M Velcro strips that are used to mount their Command Hooks. hey seem to be much higher quality.