This limerick on Whistler seems to allude to his expulsion from the Burlington Fine Arts Club in December 1867 as a result of his combative behavior earlier in the year with several people, most pertinetly with his brother-in-law Seymour Haden. See
Fredeman, Correspondence 67. 55, 80, 169).
A general commentary on DGR's limericks and their context is available.