In the sentence, "We let the dog into the yard, and it checked out the new territory.", you can only use "checked out." "Checked", "checked up", and "checked on" would not be right here - these words are used with a human subject (and often in a technical sense) and can't be used with a dog. "Checked out" can be used with a human or a dog - this is a friendly verb that has much more flexible usa