Apparently, because the top will not be tight if the [tension band] straps are unattached, not only will the top not stay clear off the rollbar hoops, but the rear glass window, headliner and outer skin will be unstable, and flop around in the wind. It is reassuring to realize that this can be properly fixed though, without relying on the dealer!
The referenced straps are shown in this Mopar parts view:
Steve Kantner offers the cause and solution here:
I just fixed mine today. The straps weren’t securely attached at the factory. You can reach in and find the straps between the internal and external fabric. The bolt they attach to is behind the plastic trim in the roof compartment. There’s a slit in the fabric to allow the strap through.
Once you get the straps through the slits, remove the plastic trim panels, remove the 10mm nut, place the strap’s hole over the bolt, reinstall and tighten the nut, and finally – reinstall the plastic trim panels.
Bonus: Links to other Convertible Top sections of the Mazda Service Manual (not applicable for simply fixing the straps though):
(See CONVERTIBLE TOP ADJUSTMENT.)
(See TOP FABRIC REPAIR.)
⇓ This photo is invaluable! Because one like it isn’t in the Fiat Service Manual, which might explain why many Fiat dealers are not installing the straps, when replacing convertible tops in their shop.
⇓ Matt (coast) provided many photos in an informative Mazda forum soft-top repair thread, that shows a properly installed bracket securing the top to the body, adding:
… you can see the black metal brackets. These fit over studs on the car and they are very difficult to get back on tightly – the new top does not want to stretch all the way. It was physically difficult to hold the top fabric tight, get the bracket on correctly, and then get the nuts on the studs. Then the nuts need to be tightened down.
⇓ Here is where that last frame hoop is supposed to be: