Reeve (1849) mentions the presence of 3 specimens in the collection of Joseph Banks, yet no type material has been traced back as of today. An unpublished manuscript by A. Warén (NRM, Sweden) suggests synonymy with T. clathrata Kiener, 1843.
Tryon (1886:206) places Reeve's name in synonymy of Kiener's T. clathrata without discussion or explanation, and shows (Pl. 64, figs. 2, 16) the figures of the respective authors to prove his point. Hedley (1907:501) compares Reeve's species to his own T. captiva and differentiates them by the number of whorls per length. Whilst Finlay (1927:496) (unnecessarily?) replaced Kiener's species name by T. iredalei, it appears that further - ongoing - research might show that Reeve's, Hedley's as well as Finlay's specific names could refer to a single species.