“inner room.” A room in the interior of the house. Calling it a “closet” misses the point, since most people think of closets as a place to store clothes. Jesus was saying to go into an inner room where no one would see, so your devotions could be private.
“repay you.” The word “openly” occurs in some versions but was added by scribes to some Greek texts. It was not in the original text (See commentary on Matthew 6:4).