Yes, you can change the order of the tribute types when adding or editing a gift. Click on Select Tribute Type and then click on “New/Edit”. 

Find the value that you want to re-order and hover over the icon with 3 rows that is to the left of the value. Drag the value to the new location in the drop-down and drop it in the new location. Click Close on the bottom left corner of the pop-up window and the changes will be saved.