smudge

Etymology 1

noun

1. A blemish or smear, especially a dark or sooty one.
   There was a smudge on the paper.
2. Dense smoke, such as that used for fumigation.
3. (US) A heap of damp combustibles partially ignited and burning slowly, placed on the windward side of a house, tent, etc. to keep off mosquitoes or other insects.
   Then "smudges" are in vogue,—heaps of damp combustibles placed on the windward side of the house and partially ignited, that their inky steams may smother the mosquitoes while we take our chance. I have had a "smudge" made in a chafing-dish at my bedside, after a serious deliberation between choking and being devoured at small mouthfuls; and I conscientiously recommend choking, or running the risk of it, at least. 1842, Caroline Mathilda Kirkland, Forest Life, volume 1, page 144
   We had taken about ten pounds of trout; and the first procedure, after reaching the camp, was to build a smudge or smoke-fire, to drive away these abominable gnats, who, fortunately, take flight with the first whiff of smoke. 1859, John Russell Bartlett, anonymous quotee, New York Courier and Enquirer, date unknown, quoted in Dictionary of Americanisms, 2nd edition, Boston: Little, Brown and Company, page 420
   The use of smoke (or "smudges") against the attack of the mosquito is well understood in America and elsewhere. May 24, 1901, H. Watkins-Pitchford, “Horse-sickness investigation”, in The Agricultural Journal and Mining Record, volume 4, number 6, page 161
4. (paganism, especially in the phrase "smudge stick" "stick of incense") A quantity of herbs used in suffumigation.
   Devil's dirt or asafetida ground together with fenugreek and black cumin seed is used as a smudge against witches and […] 2006, Christian Rätsch, Claudia Müller-Ebeling, Pagan Christmas: The Plants, Spirits, and Rituals

Etymology 2

From Middle English smogen.

verb

1. To obscure by blurring; to smear.
2. To soil or smear with dirt.
3. To use dense smoke to protect from insects.
4. To stifle or smother with smoke.
5. (paganism, intransitive) To burn herbs as a cleansing ritual (suffumigation).
6. (paganism, transitive) To subject to ritual burning of herbs (suffumigation, smudging).
   This is easily done using incense to smudge yourself or taking a cleansing bath. To smudge your body use an incense mixture such as sandalwood, lavender, frankincense or myrrh. 2013, Rachel Patterson, Pagan Portals - Hoodoo: Folk Magic