Churg-Strauss Syndrome lies within the spectrum of Wegener's Granulomatosis, microscopic polyangiitis, and ANCA-associated vasculitis: all diseases which result from inflammation of small-to-medium-sized vessels. The "classic triad" of Churg-Strauss syndrome is asthma, eosinophilia, and vasculitis, and although "renal involvement" is not amongst these, it does occur in a subset of Churg-Strauss patients.
In this 2006 AJKD article looking at 116 Churg-Strauss patients, about 25% had some type of renal involvement. Of those who had rapidly progressive glomerulonephritis and crescents on biopsy, all were ANCA-positive. Renal involvement in Churg-Strauss should therefore generally be managed as an ANCA-associated vasculitis, e.g. steroids, Cytoxan, with a possible role for for plasma exchange or Rituxan.