I assume you are using the online family tree editor (rather than our family tree software Family Tree Builder).
The online family tree editor has a drawback which is, if a genealogy card (that is what the square is called) is connected to other genealogy cards, it cannot be removed without deleting all other connections until the person you wanted to delete has no one else connected to him or her.
Think of a chain. If you wanted to remove a link in the middle of the chain you would have to start removing links from one end of the chain in order to reach the link you originally intended to remove. You couldn't simply take out the link in the middle.
(We are going to release a new version of the online family tree editor in the near future with a better solution to this. We've already started working on it.)
I understand that in some cases removing many people in order to reach one mistake can be a lot of work. There is another solution which is to use our family tree software Family Tree Builder. The operation takes several steps and I recommend it only for people who have a good grasp of computers and importing/exporting files. If you feel you would like to learn how to move your tree into Family Tree Builder, let me know and I'll explain.