This root appeared only in very late notes on Quenya verbs from 1969 (PE22/166), where it was given as an alternative to √ATHA, a root Tolkien introduced back in late 1950s or early 1960s to explain Q. asëa aranion/S. athelas “kings foil”. In the 1969 note, Tolkien at first reaffirmed that √ATHA was the basis for these words, but in the margins he wrote:

This needs correction. √ATHA = be willing, agree, consent, grant — assist, join with others[?]. It is HATHA, Q haþa- that meant treat kindly/make easy, (help to) cure (PE22/165-166, note #109).

On the back of the page Tolkien then explored various possible derivatives of the new root √HATHA, among them Q. {asea} >> aþea but also Q./T. haþa- “treat (medically)”, various Quenya words for “doctor” (aþumo >> aþar(o); aþarta) and several Sindarin forms including {gathra} >> athra, which seems to be another verb meaning “to treat medically” (PE22/166 note #110). The presence and absence of initial h- in the Quenya forms and the presence and absence of initial g- in the Sindarin forms are probably a reflection of Tolkien’s indecision in the late 1960s on the proper phonetic development of initial velar spirants in the Elvish languages; see the entry on how initial [ɣ] became [h] in Ancient Quenya for further discussion.

For the most part, Tolkien had initial primitive h- survive in Quenya, making the derivation of Q. asea “healing herb” directly from √HATHA problematic. But perhaps Tolkien intended that √HATHA was blended with √ATHA to produce asea; something similar happened with the root √HAN “add to, enhance” in these same 1969 verbal notes, which influenced Q. anta- “give” (PE22/163). In any case, √HATHA is our best source for Elvish “doctor” words, and it provides a useful semantic distinction from √ATHA which has more varied roles, serving among other things as the basis for the Sindarin future suffix -atha (PE22/167).