Does yours have some function to bend it the other way and push the bits out? I always ended up having to scoop out the stuck bits and it is so much more work than squishing the garlic with the side of a knife. But I admit it may have small lumps. I normally squish, peel off the skin, slice against the grain, and squish again.
Takes about 10 or 20 seconds, nothing extra to clean, and the biggest bits are still pretty small.