It would be easier to investigate if the behavior can be replicated. You could try reloading the template or Word (and I believe Microsoft has an Office cleanup tool that checks for corruption).
#Avery print templates for word how to
So that's what it is, and you raise the questions of why it appears in multiple locations, why the first sheet is different from subsequent sheets, and how to hide it (or make it less confusing for the users). It is actually controlled by the operating system rather than Word. It marks the text insertion point and can be used for text selection. You added clarification in a comment on the question that you are interested in the "I-beam" cursor. Good discussion of the formatting symbols and controlling them can be found here (these images are from that link). The keyboard shortcut Ctrl + * should also work.
One is accessible through the paragraph marker symbol on the Home tab: There are several ways to control display of formatting marks. I don't have ready access to Word, but if I remember correctly, this is not one of the symbols that has an individual override option (displayable even if formatting marks are off). You should be able to switch display of the symbol on or off with Show/Hide formatting marks. It is displayed in cells and it marks the end of the last paragraph in the cell or the end of the cell.