If we want more persuasive evidence of test of controls, that means more reliable evidence of test of controls
then we should increase extent of checking   
further if want higher degree of reliance on internal controls then we need more persuasive evidence 
so correct relation is more persuasive evidence = increase test of controls
higher degree of reliance = more persuasive evidence 
but MCQ is not properly drafted, hence students get confused 
 

MCQ is not properly drafted by ICAI
More persuasive evidence = Means auditor wants more reliance on controls = So increase extent of checking
Collecting more persuasive evidence will give higher degree of of reliance on controls
MCQ want to say for more persuasive evidence go for higher degree of reliance on controls that looks inappropriate 
 
auditor 1st decides how much reliance he wants on internal controls then he decides how much persuasive evidence and extent of checking for it is required