I cannot recognize what type of formatting element it is in this Word document and how to get rid of it

The square brackets represent bookmarks. Your document has an hidden bookmark. Opening it with LibreOffice Writer, then Insert -> Bookmark shows that there are more than one bookmarks (see first screenshot). Pressing Ctrl+A to select them all then clicking on Delete, remove them all.

On MS Word, Insert -> Bookmark. Select Hidden bookmarks to display the bookmark on the list. However, it only shows a single hidden bookmark (see second screenshot).

I started telling you they are bookmarks Then I checked your file and they are not bookmarks. They do not print. They are not Content Controls.

Unless you have some code that fills out your form, you can certainly delete them. Place your cursor after them, in the same cell, and backspace.

Was this form imported from another file type or program?