You're not going to get any of price of the ticket refunded as you accepted the alternative airport and flew into another New York metro (EWR. LGA, JFK) airport. If you incurred expenses (gas, tolls, time, etc.) to travel from Newark to JFK to retrieve your bags, have receipts and send copies with a letter requesting reimbursement. If they fail to do anything for you then consider filing in small claims court if you think it's worth your while.
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