I wrote about this in my article on the Vladimir tiara:
In my opinion, the whole thing is a fabrication, invented by the press to pit Meghan against Eugenie.
There was this terrible, inaccurate documentary on Channel 5 about British Royal Jewels where they brought it up as well that ended up completely contradicting itself.
Apparently, Princess Eugenie had 'earmarked' the Greville Tiara, always knowing that she (being a princess) would wear a tiara on her wedding day. They then tried to make a point that Meghan was only allowed to wear a tiara from the 'third class' and Eugenie got to wear one from the 'first class'.
If that were the case, then why has the Greville Emerald Tiara only been worn by the 10th in line to the throne the whole time it has been in the Royal Family. The documentary then says 'Neither women got the tiara they wanted so Eugenie wore the Greville Emerald Kokoshnik'. So what on earth were you just talking about??? .
Then there's the part about the 'unknown Russian provenance'. The Vladimir has a clear provenance as well as evidence for payments and authentication from Cartier in Paris.
If there is another Emerald Greville tiara then I really think we would've seen it by now.