I've been taking garlic tablet for some years now, and have never had a problem regrding burping or tasting garlic when taking them.
I've never heard about the fact that they are supposed to prevent insect bites though. I take them as I had high blood pressure and heard that garlic was used for many conditions including high blood pressure, high cholesterol, narrowed arteries, etc, but insect bites - never!
As I'm treated successfully by my doctor for various conditions due to type 2 diabetes, I can't claim that garlic tablets are the answer, but I will continue to take them.
The garlic tablets I take are purchased as part of my supermarket shop, and can honestly say I have never experienced the problems stated by jakep.