You don't need to lift a finger, but you do need to recognize that any "returned" mattress is likely going straight to a landfill.
And some anecdata: When I wanted to return an online mattress, I had the option of showing a receipt for giving it to a charity, or having the mattress company pick it up. None of the local charities I looked into took even slightly used mattresses. So the mattress company "pick up" was from a junk disposal company, and they just took the mattress to the waste transfer station on its way to the landfill.