(literally) To make foul; to soil; to contaminate, pollute.
1897, Robert Gwynneddon Davies (translator), The Sleeping Bard by Ellis Wynne, London: Simplkon, Marshall & Co., Part I,
At last, what with a round of blasphemy, and the whole crowd with clay pistols belching smoke and fire and slander of their neighbours, and the floor already befouled with dregs and spittle, I feared lest viler deeds should happen, and craved to depart.
1997, Ted Hughes, Tales from Ovid, “Echo and Narcissus” in Paul Keegan (ed.), Ted Hughes: Collected Poems, New York: Farrar, Straus and Giroux, 2003, p. 919,
There was a pool of perfect water.
[…] No cattle
Had slobbered their muzzles in it
And befouled it.
To stain or mar (e.g., with infamy or disgrace).
To entangle or run against so as to impede motion.