I am surprised that they could build their garage right up to your property line.

How big is your yard? How much room do you have to plant things that will cover the garage?

Can you post dimensions and some pictures that show us more of what we have to work around?

You can see there are actually two garages.

Fence across, whole or partial portions, with climbing vines.

"I am surprised that they could build their garage right up to your property line."

Maybe Dani v's fence is on their property?

A fence always makes for good neighbors and then plantings in front of it . Add a trellis type top to the fence and plant at least some vines to grow up and run through the trellis .

Since the neighbors do not see the back of their garage, you could approach them about painting them a darker less obtrusive color and then add some plants.