"Tactful way" refers to the way you communicate or act in a sensitive and considerate manner, so as not to offend or hurt someone's feelings. Full definition
There are definitely ways to celebrate a non-religious xmas, but there are certainly more tactful ways of saying it. (religion.blogs.cnn.com)
I personally don't agree with how some of those billboards come across — I think there are more tactful ways of saying that you don't have to be christian to celebrate xmas. (religion.blogs.cnn.com)
Probably the most tactful way to describe the procedure is that it involves shooting as much as 15 gallons of water into your colon, through a tube inserted in your rectum. (businessinsider.com)