The unglossed root ᴱ√SḶTḶ appeared in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. silt- “sift, sort out, winnow” and ᴱQ. silta “sieve” (QL/84). Gnomish words G. thlid “sieve” and G. thlid- “to sort out, sift, sieve, discriminate” from contemporaneous Gnomish Lexicon are clearly related, and the archaic past form salti (later thlinti) confirms the root was actually ᴱ√SḶTḶ (GL/73). A last hint of this root can be seen in ᴱQ. silte “sift” < ᴱ✶sḷt- with past salsie, a verb form appearing in the Early Qenya Grammar of the 1920s (PE14/58).
Neo-Eldarin: I think it is worth positing a Neo-Root ᴺ√SILIT “sift” to salvage some of these early words.