。
She took up his offer.
Literal
She [topic-は] his [genitive-の] offer [object-を] took-up.
取り上げる is a 複合動詞 from 取る ('take') + 上げる ('lift, raise') — literally 'pick up.' Has multiple specialized senses depending on context: 'take up (a topic), feature/cover (in news), confiscate, accept (an offer), or just literally pick up.' Here, with 申し出 as object, it lands on 'accept the offer.' Compare with 受け入れる ('accept, take in'): 取り上げる is more 'engage with/treat seriously,' while 受け入れる is 'accept and incorporate.'