。
She made the offer as a token of gratitude.
Literal
She [topic-は] gratitude [attributive-の] sign [as-として] that offer [object-を] did.
感謝の印 ('a sign / token of gratitude') is a fixed phrase in Japanese gift-giving and ceremonial speech — the kind of language used when handing over a present, sending a thank-you note, or making a gesture in return for kindness. 印 here means 'sign / token / mark,' not 'seal' (which is the more familiar everyday meaning). ~として ('as / in the capacity of') pairs the gesture with its function: the offer *plays the role of* gratitude. 申し出 ('offer / proposal') comes from the humble 申す ('say [humbly]') + 出る ('come out') — etymologically 'something that comes out [of one's mouth] humbly,' which fits the polite act of formally proposing to do something for someone.