How do I remove items from my wardrobe?

In the old wardrobe, you can put the items on your HA, then check them off and click "Checked to Inventory" (note that the items generally don't disappear from your wardrobe, but they should still be moved to your inventory). You could also go to the Wardrobe section on the left-hand side (Avatar - Clothes - Wardrobe), search the items you want to remove and click the >>> button, then move to Inventory.

In the beta wardrobe, I think you have to use the Items button at the top (Save - Outfits - Items) but I don't really use the beta so I'm not sure what else you have to do from there (and iirc that menu always took forever to load for me anyway)

I am on the old version where it says your clothes on the left and move clothing on the right they are both blank

It takes awhile to load sometimes. Otherwise it might just be easier to go into the Clothing section and do it that way if you're only removing a few items