Is it harmful for the fish if you remove the temp. indicator if its inside the tank with fishes inside?

Are you talking about one of those self adhesive thermometers? Not sure if the glue used would be safe for the fishes or not, so just to air on the side of caution.... I would definitely lower the water line if possible before attempting to remove it. You may need top use a razor blade to remove it all-keep the glass wet while using a blade on it so it doesn't scratch.