scrub v.

c. 1400, scrobben, "to rub hard; rub or scratch (someone, an animal)," a variant of shrubben (c. 1300), which is perhaps from Middle Dutch or Middle Low German schrubben, schrobben "to scrub," or from an unrecorded Old English cognate of these, or from a Scandinavian source (such as Danish skrubbe "to scrub"). Probably ultimately from the Proto-Germanic root of shrub, an ancient cleaning tool. Compare the evolution of broom, brush (n.1), also compare scrub (n.1).

Meaning "to cancel" is attested from 1828, probably from notion of "to rub out, erase" an entry on a listing. It was popularized during World War II with reference to air missions. Related: Scrubbed; scrubbing.

late 14c., "a low, stunted tree; a shrub," variant of shrobbe, from Old English scrybb, scrub (see shrub, which is the common form of the same word),  perhaps influenced by a cognate Scandinavian word (such as Danish dialectal skrub, Old Danish skrubbe, "a stunted tree, brushwood").

The collective sense of "brush, stunted trees, shrubs; a tract of these" is attested by 1805. Transferred sense of "mean, insignificant fellow" is from 1580s; earlier it meant a small breed of cattle (1550s). The U.S. sports meaning "athlete not on the varsity team" is recorded from 1892, probably from this "insignificant" sense, but compare scrub "hard-working servant, drudge" (1709), which is perhaps from influence of scrub (v.).

As an adjective from 1710, "of inferior breed or stunted growth," from the noun. Scrub oak for a kind of low American species, is recorded from 1766. 

1620s, "act of scrubbing," from scrub (v.). Meaning "thing that is used in scrubbing" is from 1680s. By 1952 as "act of cancellation, an abandonment."