Clumpy yogurt conundrum
You want the garlic flavor but not the chunks of garlic?

You can crush your garlic and let it sit in a couple tablespoons of warm olive oil for a while. Remove the garlic and whisk the now-flavored oil into your sauce. Besides adding the garlic flavor, the oil will also make your sauce develop a beautiful, glossy sheen.

Personally, when I make similar sauces, I just crush my garlic and mince it fine. There are very small chunks in the sauce but they are impossible to see and only rarely felt on the tongue. I don't find it objectionable.