I'm surprised no one called the cops on this customer; however, I agree with others who state it was absolutely totally inappropriate for the Door Lady to grab the woman's purse.
I have never been in a Costco but I know Sam’s does not bag any items they go back into the cart just like when you take them out at the register. They have to at least make an effort at the exit door to check you went throught the check out process and paid.