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She doesn't even glance at the offer.
Literal
She [topic-は] that offer [target-に] glance [even-も] not-do.
見向きもしない (lit. 'not even do a glance toward') is an idiomatic expression of total disregard — the も intensifies the negation to 'doesn't even bother to.' Built from 見向き ('a turn-of-the-head glance') + も + しない. The に marks the target of the (non-)glance: 'doesn't turn her head toward the offer at all.' Stronger than 拒絶する ('refuse'), this conveys not just rejection but disinterest at a level that doesn't even acknowledge the offer's existence — the kind of cold dismissal that can sting more than an outright no.