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”.
An “unspoken name” of Varda in some linguistic notes for the early 1950s (PE21/82). Its meaning is unclear.