This root was connected to grabbing things by hand for most of Tolkien’s life. It first appeared as ᴱ√MAPA “seize” in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. map- “seize, take” and ᴱQ. maptale “robbery” (QL/59). In the contemporaneous Gnomish Lexicon its main derivative was G. mab “hand” (GL/55). In the Gnomish Lexicon, Tolkien did redefine mab as a dual form of G. mô “hand”, but it was later restored as an independent word and survived all the way into Sindarin as S. mâb “hand”.
The root reappeared as ᴹ√MAP “lay hold of with hand, seize” in The Etymologies of the 1930s with a similar set of derivatives (Ety/MAP). √MAP was mentioned again in the late 1960s in notes on Eldarin Hands, Fingers and Numerals, with glosses like “take hold of, grasp” (VT47/7) and “take away” (VT47/20). But in these same notes Tolkien made the somewhat shocking decision to abandon this root, proposing instead that S. mâb was derived from CE ✶makwā “handful” (VT47/6).
Neo-Eldarin: For purposes of Neo-Eldarin, I would ignore this very late idea, since √MAP appears so regularly in Tolkien’s earlier writings.