The correct answer is:
Katherine and her partner were right, and the server should get a second serve.
From The Code, Item 42:
Item 42 states that each player is responsible for removing stray balls. However, a server may serve with stray balls on the court if they were not removed before a point. The server’s partner can’t demand a new first serve because she decides that a stray ball needs to be cleared after a point has already been played.
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