I can't say for certain because I don't know what's in your template, but
most calendar templates in Word are built with tables. The lines are borders
of the table cells. So to change the color, you select the table and click
Format > Borders and Shading. On the Borders tab of the dialog, make sure
the Apply To box says "Table" (not "Cell" or "Paragraph"). Then open the
Color dropdown and choose the black square (or, usually, Automatic is
equivalent to black).