How would you remove T-Shirts from a Character?

Part of the script I have below removes only have of the T-Shirt on the character, how would I make/add another part of the script to remove the T-Shirt completely?

if speaker.Character:findFirstChild("Shirt Graphic") then
	speaker.Character["Shirt Graphic"]:Destroy()
end

thing = speaker.Character:FindFirstChild("ShirtGraphic")
if thing ~= nil then
	thing:Destroy()
end

-Goulstem