Somewhere in the tree of objects of the object you're trying to map TestComplete was unable to find an object. Say for example you have the following line
Aliases.MyWebPage.MyGridTable.MyControl
If MyWebPage does not exist when I'm trying to edit MyControl, I'll get the message "The underlying object does not exist" You'll need to do some investigation to find where the object recognition falls down and correct that.
If I'm trying to edit MyControl and MyControl is present currently in the application, I'd get that message as well.