3M might make a specialty tape that will stick to the polyethylene but the bond won't be great. I had to attach some baby locks to some polyethylene boxes in our cubby bench and even their VHB tape wouldn't stick. I finally had to torch the boxes to get the tape to stick. Torching changes the molecular structure of low surface energy plastics like Vision uses and allows some adhesives to stick. But even then the bond isn't great.
But don't let it frustrate you, it's these same characteristics that makes Visions and other cages built from LSE plastics to be so easy to clean.
But back to the point at hand, I would never torch a nice Vision cage and like Randy said I would never use tape. If that background popped off the cage you'd have a very real risk of a reptile getting stuck to some very nasty tape.
And for the record, silicone won't bond well either.
Other than the thin bolt idea, you could also epoxy a few runs of fishing line or something to the background and have it exit the back of the cage through tiny holes. You'd then tie it around the back. But I'm not crazy about that idea either, although it would mean for smaller holes in the cage. If you try it you'd have to take care that no small gaps were left between the line and the cage and/or background for a tail or a claw to get caught in (don't remember if you said this was for snakes, lizards, or what).
I guess I like the idea of thin carriage bolts run through the back and into nuts epoxied into the back of the background.
Or maybe call 3M and see if any of their two-part caulks will bond to the polyethylene. Before you do that call Vision and clarify what plastic blend they use. And maybe they'll know of something that will work.
With a caulk if the BG pops off at least it will be cured and the risk of an animal getting stuck to it is eliminated, unlike the tape idea.