The Collaborative International Dictionary of English v.0.48:

Burl \Burl\ (b[^u]rl), v. t. [imp. & p. p. Burled (b[^u]rld);
   p. pr. & vb. n. Burling.] [OE. burle stuffing, or a knot in
   cloth; cf. F. bourlet, bourrelet, OF. bourel, a wreath or a
   roll of cloth, linen, or leather, stuffed with flocks, etc.,
   dim. of bourre. [root]92. See Bur.]
   To dress or finish up (cloth); to pick knots, burs, loose
   threads, etc., from, as in finishing cloth.
   [1913 Webster]

   Burling iron, a peculiar kind of nippers or tweezers used
      in burling woolen cloth.
      [1913 Webster]