Avis toll transponders always are in an enclosure located near the base of the rear view mirror. If you close that box, the transponder doesn't work anymore and you can use your own.. That is very reliable.
You do not need to declne Avis' tolling. The "E-Toll standard" plan that you're automatically enrolled in will not incur any fees unless you're using their transponder or drive through a tolling-by-plate road without having your own transponder activated. Just make sure your transponder is working and the Avis one is in its closed box.
This works. Just look around this forum, there'd be tons more posts otherwise.