If an Oyster card does not have sufficient credit to cover the Gatwick Express fare then it won’t open the gates to platforms 13-14 at Victoria. You would need to seek assistance. Your paper ticket won’t work the barriers either.
I would not recommend repeatedly asking TfL to refund Gatwick Express fares. They are likely to refuse after the first couple of requests because they will have explained that you can’t use the Oyster card in that way.
I repeat my earlier advice that you need to ask GTR customer services how to make the journey you require using the valid tickets that you have.