A microwave oven works by subjecting its contents to an intense electromagnetic field which changes direction about 5000 million time a second. This is real handy for cooking food since food has significant water content and water molecules have a positive electrical charge on one end and a negative electrical charge on the other. The alternating electric field shakes the water molecules back and forth, imparting energy which shows up as heat.
Material which does not contain much water and does not conduct electricity, like air and crockery, is pretty much unaffected by microwaves. Electrical conductors appear to reflect microwaves because the electric field of the wave induces electrical currents to flow in the conductor. These internal currents alternate at the same frequency as the incoming wave and re-radiate a wave that looks like the original. Semiconductors also have electrical currents induced in them by the incident wave. Because semiconductors have higher electrical resistance than do conductors, the internal currents generate considerable heat.
A hearing aid is a collection of insulators, conductors and semiconductors. Subjecting one to microwaves is very likely to cause electrical currents and heat sufficient to destroy the semiconductors and generally cause arcing and sparking around the inside of the device. I would recommend that if your dog takes your hearing aid in his mouth and later gives it back, which by the way is only one possibility, take the battery out of it, rinse it off in clean water and set it in a dry warm place for a day or so to dry. That might restore it...or perhaps not.