There is no infinitive in the sentence, and in any case there is nothing wrong with splitting infinitives.
I am not sure but it’s ‘to hand over something to someone’ and not ‘to hand something over to someone’
either returned or handed over is more accurate than "gave" to my thinking
No Susan, “to hand over” is an infinitive, but in this context “to” is a preposition and there is no infinitive to split. Arguably it splits a compound verb, but it is common in native English to do so. And as per Seenoff’s question, I’d like a DL moderator or native French speaker to explain why “returned” is wrong in this context.