。
She sent a telegram saying she'd come right away.
Literal
She [topic-は] right-away go [quotative-と] telegram [object-を] sent.
電報を打つ ('send a telegram') uses 打つ ('to strike') — a holdover from the days when telegram operators physically struck telegraph keys. The verb 打つ generalizes to any short-burst transmission action: メールを打つ ('type / send a message'), 注射を打つ ('give an injection'). Telegrams in Japan, sent via 日本電信電話 (NTT) and predecessors, were a major communication channel from the Meiji era through the postwar period — used for urgent news, short greetings, and condolences. Today they survive mostly for ceremonial purposes (weddings, funerals).