Luggage with an ITH tag will be delivered (eventually) to ITH. The only other possibility is that it will be re-tagged to SYR to match her flights (unlikely, not not impossible). If it were to get offloaded in EWR, they would still be on the hook to deliver it to ITH, since that's where it's tagged. She should check the carousel in SYR, and, assuming it doesn't arrive, she should file a delayed luggage claim. She should have the option to have the bags delivered to her in ITH or to pick them up at the airport if she prefers.