How to dry fruit peels without growing mold?
You can't close them up and expect them to stay mold-free, they will produce too much humidity. 

You will have to spread the peels on a flat surface, without overlapping. Do it on a slightly absorptive surface, and breathable is good too. The optimal setting would be a wire rack with a sheet of paper on it, but if you don't have a rack to commit to the task, skip the breathable part and use a large plate. 

While you can't have them conveniently stuffed in a jar, they are not so hard to get dried. Just don't use prime real estate such as the kitchen counter. Find a convenient, undisturbed wide place - the top of a cabinet works, if you put something above them to keep the dust out. Or maybe you have some surface which is flat, but too low to be used for anything else. As long as there is free air flow, there is no problem of having something close above them. 

Or, as tM-- suggested, use a quick drying method. Both an oven and a dehydrator should work. You will get a slightly better taste with slow air-drying, but the difference may be too small to notice. 

Once the drying is completed, the peels can easily be stored in a jar without catching mold.