The Collaborative International Dictionary
Begriming
Begrime \Be*grime"\, v. t. [imp. & p. p. Begrimed; p. pr. & vb. n. Begriming.] To soil with grime or dirt deeply impressed or rubbed in.
Books falling to pieces and begrimed with dust.
--Macaulay.
Wiktionary
begriming
vb. (present participle of begrime English)