My labrador once ate a whole meatloaf I left on the counter. I was more upset about losing DINNER than his weird burps, which is pretty sad when you think about it. Like @the_susan said, at least it's not something worse, but my wallet felt the hit from ordering pizza all week. That dog had garlic breath for days, let me tell you.
You sure that's a bad thing? Garlic in tiny amounts can be fine for dogs and herbs might help his stomach. That burp smell probably beats regular dog breath anyway. Could have eaten something worse during the reno.
Did your pup get into the spices during a kitchen reno too? Mine found a whole jar of oregano once and let me tell you, his burps smelled like pizza for a day. I called my vet in a panic but they just said to watch him and maybe give him some plain canned pumpkin to help things move along. What did your vet say when you called them?