How do you remove tile soap dish without damaging other tiles?

I would try getting Goof Off under the soap dish. I would scrape away at the grout around the soap dish and then squirt on some Goof Off. Goof Off removes glue, paint, ink, and so on. I would squirt on some Goof Off, dig a little, squirt some more, dig a little more, and so on. Home centers and hardware stores sell it for less than $5.