Definition of "thallophyte"

They[algae, fungi and mosses] lack the vascular tissues; thus, they are called thallophytes. Algae are thallophytes with chlorophyll. […] Fungi are thallophytes without chlorophyll.

1994, Estrelita A. Madriaga, Anthony Lee, Felicitas B. Ventura, Orlando A. Oronce (coordinator), Biology: Science and Technology II, page 347

In general, the usefulness of the thallophytes as Hg bioindicators was limited by their sporadic occurrence in the forest environment. Because of the importance of the thallophytes as components of the food chain, however, several samples from different groups (summarized in Table 2) were collected for comparison with values reported in the literature.

1994, Pat E. Rasmussen, Chapter IV.5: Mercury in Vegetation of the Precambrian Shield, Carl J. Watras, John W. Huckabee (editors), Mercury Pollution: Integration and Synthesis, page 422

Fossile[sic] records along with molecular, cytological and morphological phylogenetic work favour a single origin of land plants from charophycean thallophytes, and indicate that several major lineages of vascular plants had evolved more than 400 million years ago.

1999, R. G. Hermann, “The Chloroplast: Part of the Integrated Genetic System of the Plant Cell”, in Joan H. Argyroudi-Akoyunoglou, Horst Senger, editors, The Chloroplast: From Molecular Biology to Biotechnology, page 66