That depends if you are referring to the gashes on your door frames from physically moving the refrigerator into the garage, or cleaning the years of gunk that have built up under the fridge, or actually running the fridge in your garage?
Believe it or not actually running the fridge in the garage could be your biggest problem.
Refrigerators at designed to work best within a room temperature range of between 60 and 100 degrees. If your garage gets colder than that in the winter (which it probably does unless you have a conditioned, well-insulated garage) it is very possible that the unit will not work properly.
Since the freezer is set to come on only when the fridge is working, it may actually warm frozen items. You probably have heard that heat is bad for frozen items. It causes thawing.
There are brands of refrigerators that are specifically made for unheated garages, but I would doubt that your old kitchen fridge would fall into that category.
Here's a bonus tip…
A lot of electrical outlets in your garage are protected by GFCI's and are not designed for a refrigerator. The constant large voltage draws caused by the compressor going on and off can fool a GFCI into thinking a short exists thus causing it to turn off the circuit.
If you are going to add a fridge to your garage, have an electrician install a dedicated, single outlet, non-GFCI protected outlet just for the fridge.