You could try reloading the template or Word (and I believe Microsoft has an Office cleanup tool that checks for corruption). It's possible that the display of multiple insertion points is a bug.Anything you would do to modify it would likely need to be done at the OS level, and would affect all text activity in all applications. I don't believe there is any way to hide them.Normally, there is only one insertion point, but for some reason, Word is showing the insertion point on each label on the first sheet. Without having the Avery template, it isn't clear how the individual labels are created (a table? text boxes? multiple small 'pages'?).I don't have ready access to Word, so I can't validate all this information. 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.

Avery templates in word 2010