Kind of crazy when people say they want a "new" diamond, uh....well all of them are literally millions of years old unless it's lab grown.
Can anyone who works in the diamond industry respond to this? Can anyone tell if a diamond has been made into a ring before? Would it damage the diamond to remove it from the ring? This sounds like an opportunity to plaster signs that say "WE BUY DIAMOND RINGS" all over and buy them back from consumers at a discount from wholesale.
The easiest way is to determine through the setting. Styles change. If it's a setting from the 50s that isn't made anymore it's probably old. If it's a setting from a company that is < 10 years old it's got a better chance of being new.
Diamonds are not damaged when swapping settings. They are often removed and reset if a prong breaks for instance.
Most people just don't want to buy from estate sales or auction. So, jewelry stores will do that, clean it up, put it in a new setting (or leave it as is), and resell it as 'new'.