。
She received a letter saying he would be back soon.
Literal
She [topic-は] [he [subject-が] soon return [that-という] gist's] letter [object-を] received.
~という趣旨の is a stock written-Japanese phrase: 'a (letter / message / decision) to the effect that ~,' with 趣旨 meaning 'gist, purport.' This is how formal correspondence summarizes its own contents inside the sentence reporting it. ~という relativizes the embedded clause as a noun-modifier of 趣旨.