| Do you ever forget things that you’ve learned before? I do. Case in point, last week I was looking at a page similar to this: 
begging the question at the top of the post. The above snip of a SharePoint 2010 site gives me almost no clue what that permission level, Limited Access, might mean. In my case, it was a SharePoint 2007 site, but they act very similar. Drilling down to edit the user’s permission gives a little more information, as shown below, but I’m still left wondering, how miwise was given this Limited Access. More to the point, How do I remove it? I clearly can’t use that greyed out checkbox to take Limited Access away. 
The answer to why is clear when you read the documentation | | - Limited Access Can view specific lists, document libraries, list items, folders, or documents when given permissions.
Note You cannot assign this permission level to users or to SharePoint groups. Instead, Office SharePoint Server 2007 automatically assigns this permission level to users and to SharePoint groups when you grant them access to an object on your site that requires that they have access to a higher level object on which they do not have permissions. For example, if you grant users access to an item in a list and they do not have access to the list itself, Office SharePoint Server 2007 automatically grants them Limited Access on the list, and also on the site, if needed. | In other words, if you’re looking to understand why a user or group has limited access, look first at the places permission inheritance has been broken, then you may find an escalated permission. To remove limited access, restore inheritance or remove the higher level permission given to the item or items. |