Those songs were both popularized by Bob Hope, but he did not actually record or sing them.
* "Thanks for the Memory" was originally performed by Bob Hope in the 1938 film *The Big Broadcast of 1938*. The song was written by Ralph Rainger and Leo Robin.
* "Memories" was written by Earle Hagen and Richard Myers and popularized by Bob Hope in the 1955 film *The Seven Little Foys*. It was actually sung by David Wayne in the film, but Bob Hope's association with the song made it popular.
So, while Bob Hope made both songs popular, he was not the original singer of either.