In September 2016 Ebay seller platecz from Prague in the Czech Republic was selling these pre euroband Estonia diplomatic plates.
All pre euroband Estonian plates, including diplomatic ones, had a debossed sticker box between the letters and numerals. These ones he has do not and so they must be reproductions rather than officially issued plates.
With so many reproductions on the auction sites these days, you have to research every plate you are thinking of buying to make sure it is genuine and used.
Just because a plate has scratches, dirt, holes or looks like it was used, always ask to see the back of the plate and check the online photo archives if you are not 100% familiar with the plates you want to buy.