。
My parents approved of my marrying Mary.
Literal
Parents [topic-は] I [subject-が] Mary [with-と] marry do [nominalizer-こと] [to-に] agreed [for-me-てくれた].
~に賛成する (to agree with/approve of) is the opposite of 反対する. てくれた is the key nuance: it marks the parents' approval as a favor or kindness toward the speaker — Japanese grammaticizes gratitude into the verb form itself.