My neighbor's grandmother was shopping at the market. Comparing prices
To the other stores with here pad and pencil. The 17 year old clerk accused her of industrial espionage and discharged her from the store. Is price checking against the law?

No, but a store is allowed to refuse patronage to anyone.

It is absolutely not against the law. There are even smartphone apps that allow you to scan the bar code and get the price at all stores (even online stores).
With that being said, stores can also refuse service to anyone they choose as long as it's not on the basis of race, gender, sexual orientation, or handicap. She should have called for a manager.
Now that the moment is over, she should contact the store's corporate offices and report the young man. He is clearly on some kind of power trip.
If they don't apologize and promise to handle it, then you should let us know the store's name and I'll begin making calls to them as well.

The manager told her she willingly and maliciously tried to damage my company by complaining and to remain silent. She ceded.

She can even post prices from different stores on the internet of she wants, and it is not illegal for other stores to send people into other stores to compare prices.

If this is a corporate store I would file a complaint to the company, and perhaps even make a deal of it on a web site.

As long as what she posts is true, there is no issues.

Very Good. She is frail elderly women and not combative. It is a local store owner from India.
She has no car, and must deal with this store owner. Thanks for the advice.