Can a legal guardian take a child out of the country?

Are you talking about a permanent move? Where are the parents? Do you have full or a limited guardianship?

It depends on the scope of the guardianship.

The answer to that starts in the court order awarding guardianship. But, in most states the guardian is not permitted to permanently relocate the child outside of the court's geographic district without the court's approval. Depending on the facts, a court may or may not permit the child to be relocated.

You keep using the phrase "Legal Guardian", and I'm not certain what you mean. A guardian, may be appointed over a person or his estate by the probate court. If the Guardian is a guardian of the person, then under some circumstances he may escort his ward out of the country. But it depends on the court, the orders of the court, and the reason for the guardianship, and the amount of money in the estate among other factors. Clearly you are concerned about something, so I would suggest you consult with a domestic relations attorney near you.