Can the IUD be pushed out of its place?

You should never remove an IUD yourself. A medical professional will be able to remove an improperly positioned IUD, though if it isn't in a harmful place, often they will leave it as surgery is more invasive than the device. If you're concerned because of pain, go see your doctor. If you're concerned because of the way the strings feel or their length, your doctor can trim them for you as well.