I just purchased 4 beautiful glass tile trivets. I want to remove the cork backing so that the tiles can be added as decor to my new kitchen backsplash. How do I safely remove the cork backing?

A good soaking in hot water should soften the cork enough so it can be flaked off with a plastic scraper. Depending on the type of adhesive used, a product such as Goof-Off or Zippo type lighter fuel may soften it enough to scrape it off as well. I think I would avoid metal scrapers, except maybe a razor blade type as a last resort, being very careful not to scratch the glass.