Tolkien (re)introduced the root √IT in 1957 to address a problem he had with the etymology of the name S. Idril. In The Etymologies of the 1930s, he based this name on the root ᴹ√ID “✱desire”, and gave it the form Idhril (Ety/ID). The problem was that in the narratives, he continued to use the form Idril, which could not be derived from √ID. In Notes on Names (NN) he wrote in 1957, he introduced the root √IT to provide a new etymology for Idril, giving the root various meanings such as “(great) enhancement”, “gleaming”, “repeat, multiply” and “glitter, shine, shimmer, twinkle” (PE17/112, 156), along with alternate forms ITH, IS and ƷIT (PE17/156). He seems to have settled on √IT and the last of the listed meanings, since in The Shibboleth of Fëanor written in 1968 Tolkien said her Quenya name was Q. Itarillë based on ita- “to sparkle”, appearing with various other it- words of similar meaning (PM/346, 348 and 363 note #42).
The root √IT was basically a reversion to the original basis for the name G. Idril, which in the 1910s seems to have been based on a (hypothetical) root ✱ᴱ√ITI meaning something like “precious”. For the effects of these revisions on other roots, see the discussion in the entry for √IR “desire”.
The root √IS was the basis for words having to do with “knowledge” for all of Tolkien’s life, as represented by the verb Q. ista- “to know” which likewise retained the same form and meaning for decades. The root first appeared as ᴱ√ISI in the Qenya Lexicon of the 1910s, where somewhat cryptically Tolkien said its Gnomish form was GIS or IS (QL/43). This is mysterious because there were no such Gnomish words beginning with gis- in the contemporaneous Gnomish Lexicon, but there is an Early Noldorin word ᴱN. gist- “to know” from the 1920s, probably derived from ᴱ✶ʒist- (PE13/144, 146); in this early period initial ʒ- > g- in Gnomish (PE12/17).
Tolkien seems to have abandoned this Noldorin variant, giving the root only as ᴹ√IS in The Etymologies of the 1930s (Ety/IS). In this form it continued to appear in Tolkien’s later writings (PE17/155; PE22/129; VT41/6; VT48/25). In one place Tolkien gave the root in inverted form √SI (PE22/134), and such an inversion appeared in some of its derivatives, such as Q. síma “imagination, mind” (VT49/16) and sinte the irregular past tense of Q. ista-. However, the majority of its derivatives are from √IS.