Alida Slade is characterized throughout "Roman Fever" as a jealous and spiteful person who wants to assert her superiority over her friend. For no reason except to hurt her old friend, Grace Ansley, who Alida is still jealous of because her daughter, Barbara, is so much more vibrant that Alida's daughter, Alida reveals a secret from long ago.
Grace has long treasured a letter from Alida's late husband, Delphin, asking Grace to meet him in the Roman Coliseum one evening. Alida reveals that she wrote the letter in order to lure Grace, who she knew had a crush on Delphin, to the Coliseum to wait in vain for Delphin and be cruelly stood up. This letter also put the frail Grace in danger of contracting Roman fever at the Coliseum, which she does, and which makes her very ill. (In other words, Alida was willing to risk Grace's life with this joke.)
This was a cruel joke, showing Alida to have been both jealous and spiteful. We could write this off as immature teenage behavior, except that by telling Grace the story, Alida reveals that she is still jealous and spiteful. She can't quite pity Grace as much as she would like and so wants to bring her down a peg or two.
However, the tables turn. Grace reveals that she wrote a note to Delphin saying she would meet him at the Coliseum—and he showed up. He might not have written the first note, but he was certainly responsive to Grace. Grace also reveals she and Delphin made love and had Barbara, turning the tables on Alida.