When intruders appear in your city limits, you can ask that they be removed. The AI will usually do this, but often, the intruder reappears the very next turn. This is because the intruder could move outside of your territory using his own movement characteristics. To counter this, you must be patient. If the intruder arrived by ship, you must wait until the ship moves away. If there is a non city space available near the intruder, you must occupy it with one of your units before asking that he be removed.
When the intruder has no avenue of escape, I think he gets removed to his nearest city which might be some distance away.
When the intruder has no avenue of escape, I think he gets removed to his nearest city which might be some distance away.