Perhaps this might help. The Carmelites are a contemplative order, founded in the early 13th century, when they received a formula vitae from St. Albert of Jerusalem. There are primarly two branches in the Catholic Church, Discalced Carmelites (ODC) and Carmelites of the Ancient Observence (O.Carm).
This group seems to be a different organization altogether. I happened to notice in their website that they put "M.Carm" after their names. I don't know if they are officially recognized, but I wouldn't dismiss them outright without further research.
Are Carmelites mystics? Yes. Two of the greatest Carmelite mystics were St. John of the Cross, and St. Teresa of Avila. Does "mystic" = "gnostic"? Not necessarily. Catholic mystics are always in communion with the Church; gnostics separate themselves from the Church.
Thank you for that helpful explanation. Although I still contend that mystics are more frequently than not associated with Gnostics in todays thinking. The push now by the universal church is to explain the mysteries in terms of a broad range of "mixed" beliefs, including those found very close to MT Carmel in the direction of Egypt...they are for the most part attributed to the Gnostics and their "influence over Jesus". Perhaps another name would lead to less confusion?
In any case. Thank you for the civil discussion.