The Collaborative International Dictionary of English v.0.48:

Thallophyte \Thal"lo*phyte\, n. [Gr. ? young shoot + -phyte.]
   1. (Bot.) A plant belonging to the Thallophyta. --
      Thal`lo*phyt"ic, a.
      [Webster 1913 Suppl.]

   2. (Bot.) Same as Thallogen.
      [1913 Webster]

WordNet (r) 3.0 (2006):

thallophytic
    adj 1: pertaining to or characteristic of thallophytes