『』。
She greeted me with "Good morning."
Literal
She [topic-は] me [to-に] 『good morning』 [quotative-と] greeting [object-を] did.
挨拶をする ('to greet,' literally 'to do a greeting') uses the noun 挨拶 ('greeting, salutation') + を + する as a light-verb construction. Greetings are considered a discrete social act in Japanese culture — there's even a verb for the act of greeting itself, distinct from saying any specific words. The double 『』 quote brackets are the more emphatic/literary set, whereas single 「」 is the everyday default. The casual おはよう (rather than polite おはようございます) signals informal context.