If we start with this sentence:
The girl gave me the information I wanted.
Then which is the right question to ask about that situation:
What did the girl give you?
What did the girl give to you?
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"What did the girl give you?" is a perfectly formed sentence. "What" is the direct object of "give", and "you" is its indirect object. This is the standard format for a question involving both a direct and indirect object.
It is also fine to say, "What did the girl give to you?" In this case the indirect object ("you") becomes the object of the preposition "to", and the verb "give" has no indirect object.
Either construction is idiomatic, and both questions mean the same thing.