Your Exchange categories will only appear in Touchdown if you have first created said category in Outlook, then have synced a contact, appointment or task labeled with that category to the device. You may choose to sync a few test items with specific categories if you want to make sure all of your categories are transferred to the device. Since ActiveSync does not support the sync of the category colors, you will need to reselect the colors that correspond with the categories on the device. To adjust those settings, go to the TouchDown Advanced Settings tab and scroll down, then press "categories." A list should appear and you can set your color preferences there. Once you've got a list of categories and the colors selected, you should be able to press menu/filter and filter contacts, appointments and tasks via category.
At this time ActiveSync does not support categories for email items. A future version of Microsoft ActiveSync will probably support email categories but until then TouchDown will not be able to offer this feature.
To remove a category you have to remove the item (calendar, contact or task) that is connected to that category in TouchDown. Once it’s removed you can go to TouchDown Settings>Advanced>Categories and select Cleanup.