The action you describe is often more associated with a street "vendor" than a shop. People cleaning your car windshield uninvited at a traffic light and then demanding money is another example. However, it isn't limited to street vendors. For example, there are restaurants, particularly in areas frequented by foreign tourists, where they will leave an unordered, apparently complimentary, dish on the table, and then charge for it.
"Forceful" is sometimes associated with this but isn't necessarily the fundamental method of manipulation. What you describe is a form of fraud, or trying to get money through deceit or manipulation. These people may escalate to more assertive tactics if the ploy, alone, doesn't work--righteous indignation, trying to embarrass you, aggression or other attempts at intimidation, etc.
Dan C's "hustler" is a good term. Another is scam artist. A "scam" is a fraudulent or deceptive act or operation - M-W
"Con artist" is related, but is typically associated with something more complex, involving multiple steps to "set up" the person being taken advantage of, while a scam can involve just a brief encounter, like your example.
A similar term that is a bit dated is flimflam: deception, fraud - M-W. A scam artist or con man used to be called a "flimflam man" or "flimflam artist".