Click inside the table for the border that you would like to change, use the breadcrumb down the bottom of the editor to select the table that you would like to change, on the breadcrumb you need to look for the table an example is listed below:

By selecting the Table option you will be presented with the option to change the border colour, you will need to set a border width for the border to appear.  

If a blue border is appearing around images with links attached to them this is because certain email clients will automatically insert a blue border around the image. What you need to do to remove this is change the border with to “0” this should then remove the border from the image.