Not sure if it still applies with fire sprinklers in the garage, but if the inspector insists, I'd run those "hoods" by the inspector and see if it would fly.

Take them out and bury the wire for now. Cut them back in and install after the fact

You don't want wires that can allow a fire to travel from your garage (car, old rags, etc) into the house -- that's why exterior walls, doors between the house and garage, etc, are held to a higher standard. It's a safety measure. Maybe the answer is Bluetooth speakers in the garage?

Two ways to do this: 1) get fire-rated speakers, they are easily obtainable. 2) install a fire-rated box enclosure behind the speakers.

Thank you everyone for your input. We think we could make a fire rated box enclosure using drywall since it is fire rated? The Keeping Room...is that what you meant? And we already have the speakers installed as we were not aware of the code. Of course it makes sense but sometimes you learn things a little too late. :)

The fire rated drywall box or they make fire rated covers for recessed lights- they look like big wool hats (they are made from felted mineral wool). My local lighting store gets them for me, we used to use them in firerated ceiling assemblies before the advent of the faux can.

Isn't this the right place for a wireless speaker?

Wireless would have been the way to go.

Here's an enclosure you can buy for example:

https://www.homecontrols.com/homecontrols/products/pdfs/NV-Nuvo/NBRKICBC-Specifications.pdf

It's not the light gauge speaker wire that's the issue, it's the speaker cones catching fire and accelerating to the ceiling and creating more fire above. So wireless speakers will not resolve the problem. Its fire code they have to be boxed in where you live apparently. Looks like you will have to dig out the drywall in the ceiling to install, not a huge job, but inconvenient.

Yes! Thank you something like this is what I was trying to find.

The Keeping Room- you are right about the way the speakers can spread the fire if not contained well and our code here. And it is inconvenient to dig the drywall out, etc but not too bad. Haha building a house isn't convenient to say the least!