The team awarded it a CHM because there was none in the AOS database and it shows up as an accepted variety in Kew's Plants of the World on-line. In POTWO, it lists Phragmipedium lindleyanum var. kaieteurum (N.E.Br.) Pfitzer and says that "This variety is accepted." Originally described as a completely different species, Kew has now made it a variety as noted above. I don't have many plants in this section, and no typical lindleyanums to compare. I attached close-ups of some of the parts. Looking through the lindleyanum awarded flowers, there is much variation among them. Also, it seems no two sources are in complete agreement.
This plant was a stud plant from OrchidBabies, of Brierfield, AL, owned by the hybridizer Earl Bailey. I bought it labeled Phrag. kaieteurum from Earl when he went out of business due to his health some years ago. He used this variety and other diminutive forms of other species to make compact his Phrags. This variety is a smaller growing plant compared to the typical variety. I do not know it's provenance prior to Earl.

A most recent world-wide publication (the bible) on Phragmipediums is titled Slipper Orchids of the Tropical Americas, by Phillip Cribb and Christopher Purver. It was published in 2017 in association with the Royal Botanic Gardens, Kew. I have attached a picture of Cribb and Purver's page in their book featuring Phrag. lindleyanum var. kaieteurum and the associated illustration plates.

On Jay Pfahl's IOPSE website, he states that "Often cited as a synonym of P lindleyanum but differs in the short status, shorter, non-branching inflorescence and certain floral characteristics, so I have included it as a separate species."

There are some other Phragmipedium hobbyists that disagree with Kew and lump them all together as just lindleyanum. It seems no two of them get along. I have seen much conflicting data and opinions regarding this section, and I have seen some indicate there isn't enough consistent differences to warrant a different species or variety status. In the end, you will have to pick which source you want to cite in if you want to go with Kew on the variation status.