It may not even be necessary to remove the line ‘I have a promise to keep, to an old friend’, since he has promised to ‘finish what he begins’ and complete the training. No doubt he believes that he has left his training unfinished yet again to go rescue Han Solo, only to be corrected when he goes to Dagobah one last time. Also, this line made it seem (to me) that Luke had spent more time with Yoda than we were led to expect given the events of ESB, so it could further imply their close friendship. In the theatrical version of the movie, it just sounds like Yoda is a friend and also happens to be old, which is rather less compelling.