The movie does not answer this (and indeed, does not even make clear that Fleck was ever even invited, this may have been entirely in his head).
I prefer to believe that the invitation was real and that Murray’s motives were not merely to make fun of Arthur. Showing the clip of the lousy performance and then having Arthur give another lousy performance live would have been bad television, and Murray is, if nothing else, a good television host.
So I like to imagine that he was hoping that Arthur could defy the studio audience’s expectations, have a successful (or even semi-sucessful) routine, and have people cheering for his bravery at taking the stage. A little bit like the William Hung experience on “American Idol”. Hung was a bad singer, but his bravery at taking the stage and his good spirit about the audience’s reaction soon won them over. Murray was, I think, hoping for something similar.