This is probably very obvious, but how do I remove it?

In the Admin panel select:

Site Information - Site Wide Settings

You will now see "Order Status Link In Order Email".

Set this to NO and you should be all set

It doesn't remove it from the website. I would like to remove it until we get the order tracking figured out.

Augie-

To remove it, under Site Information >> Site Wide Settings, set Checkout Customer Password Is Displayed to No. This will not display a password in checkout, and then remove the link from up top.