i would improve this 
a. If TrafficManagerClient.RemoveTrafficManagerProfile will throw on failed request, mostly likely, just do nothing  
b. If you would like to throw out more meaningful exception, do a try-catch-rethrow, and put the original exception as inner  exception
c. If it is indeed the case that the operation could fail w/o error, throw out a more specific typed exception such as invalidoperationexception?