Presumably a paraphrase of "A peculiar virtue in wildlife ethics is that the hunter ordinarily has no gallery to applaud or disapprove of his conduct" or of "Hunting for sport is an improvement ..." above. 
Unlikely to be by Leopold, who knew that ethics involves not only doing the right thing, but also determining the right thing in the face of competing desirable criteria. 
Misattributed
                                    
“A bottom line principle of business—and life—is, to do what is right, even when no one else is looking. Likewise, we ought to do the right thing even if others around us seem to be backwards.”
            Don Soderquist “ Live Learn Lead to Make a Difference https://books.google.com/books?id=s0q7mZf9oDkC&lpg=pg=PP1&dq=Don%20Soderquist&pg=PP1#v=onepage&q&f=false, Thomas Nelson, April 2006 p. 145-146. 
On Acting with Integrity
        
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Don Soderquist 54
1934–2016Related quotes
“Integrity is doing the right thing, even when no one is watching.”
                                        
                                        Not found in Lewis's works. 
"Integrity means doing the right thing at all times, without hesitation" is found in a 1943 syndicated newspaper column. Elsie Robinson,  "Listen, World!" https://www.newspapers.com/newspage/58360960/, Evening News (Harrisburg, PA), 1943-02-24, p. 10. 
"Integrity means doing the right thing even when no one is there to judge" is found (unattributed) in the  1965 Journal of Clinical Psychology https://books.google.com/books?id=9rm1AAAAIAAJ&dq=%22integrity%22+%22doing+the+right+thing%22&focus=searchwithinvolume&q=%22doing+the+right+thing%22. 
The quote became attributed to C.S. Lewis  by 2012 https://books.google.com/books?id=XH-1TURLaf4C&pg=PT154&dq=integrity+%22even+when%22+%22c+s+lewis%22&hl=en&sa=X&ved=0ahUKEwi6x9XznoTKAhUKymMKHdoKCKoQ6AEIHTAA#v=onepage&q=integrity%20%22even%20when%22%20%22c%20s%20lewis%22&f=false. 
Misattributed
                                    
"Doing Good — for the right reasons!" (13 March 2008) http://www.youtube.com/watch?v=8h628E1PMWY
“Integrity is doing the right thing, even if nobody is watching.”